Three years ago, the international success of Animal Kingdom - a dark, complex crime film by first-time director David Michôd - brought Weaver to the attention of the US film industry. The Australian movie won the Jury Prize at Sundance, the first of an astonishing raft of nominations and wins that culminated in Weaver's nomination for Best Supporting Actress at the 2011 Oscars. From this high point, Weaver's fortunes have only improved, and a second Academy nomination for her role in David O. Russell's Silver Linings Playbook in 2013 cemented her status as a bona fide international star.

Parkland, in which she plays Lee Harvey Oswald's deluded mother Marguerite, will hit cinemas later this month and could lead to a third round of nominations. Weaver's role in the film that tells the story of JFK's shooting is small, but she dominates every scene she is in, with a pitch-perfect Louisiana accent and fervent, deranged belief in her son. She has just returned from four "idyllic" weeks in the south of France, working on Woody Allen's latest film, Magic in the Moonlight.

Actor Kate Mulvany, an old friend of Weaver's, says Weaver "giggles her way incredulously through conversations" about her latest roles; writer Luke Davies, who got to know Weaver through Michôd, echoes this, describing her "quiet giggly gratitude".

"She keeps telling me that I've ruined her life!" Michôd laughs, and recounts the "extraordinary equanimity" with which she's handled everything that has come her way. "She's a movie star without the movie-star ego," says her manager Alex Cole, an LA-based Englishman.

Weaver's ex-husband Derryn Hinch puts it in blunt Australian terms. "She's not a show pony," he says, adding that he believes this is one of the reasons for her being embraced by Hollywood. I notice that underneath her frequently self-deprecating humorous remarks, she projects a solid sense of confidence. She never downplays her work or her abilities, I point out to Hinch. "That's because she knows how good she is," he says.

"Deep down, she knows she deserves it," Mulvany adds. "She's worked f...ing hard. She's lived life fully and fabulously, with grace and gravity."

Hinch says Weaver has dealt with success from an early age, when she scored the stage role of Cinderella in Sydney at 15 and started going out with the leading man. "She's going to school with Australia's top star, Bryan Davies, picking her up in his red Jaguar! She's been there, she's had all that. So she handles fame very comfortably."

Weaver had no international reputation when Animal Kingdom screened at Sundance in 2011. "As far as Hollywood was concerned, she was a newcomer," Michôd explains. "You could feel people quickly coming to realise that Jacki wasn't some lady who had been pulled out of the supermarket, that she was a kind of Anglosphere acting royalty that they hadn't heard of."

In the film, Weaver's character Janine "Smurf" Cody is at the centre of a criminal gang of armed robbers and drug dealers, a manipulative psychopath in the guise of a smiling, suburban woman. "I loved the idea of a quite dangerous and powerful woman being packaged in a diminutive and delightful grandmother figure," says Michôd, who wrote the role specifically for her. "As soon as I put it in those terms, there was no one else but Jacki."

American audiences were able to see her performance without understanding how much it went against type, in many ways, for the well-loved woman whom many of us think of, as Davies puts it, "as a red-carpet fixture on the arm of Hinch". They "hadn't grown up with 'adorable Jacki' ", explains Brett Sheehy, artistic director of the Melbourne Theatre Company. This meant, he says, a fresh perspective on "the depth of her talent".

Cole knew nothing about her when he saw Animal Kingdom, just before the film had started to attract serious awards buzz. He immediately wanted to work with her, but recalls feeling "intimidated" at the prospect of meeting her, even though meeting actors is what he does for a living. "She can be so disarming. You wonder, how can a woman portray this role so convincingly? You think there has to be some element of a twisted mentality there, yet the moment you see her, she's soft as a feather." Weaver is now godmother to Alex's second child, Harley - a role Cole says he wanted her to fill because of her combination of being "streetwise" and "really wise".

Weaver is anxious to dispel any perception that her career was in the dumps before the Oscar nomination. "It's a nice Cinderella story," she says, "but it isn't true." After Animal Kingdom finished shooting, she appeared onstage in six plays in 18 months. But "in Australia, if you're not on television people think you've disappeared". She's never had trouble getting work in live theatre, but quality roles in movies were much harder to come by. "Her passion was always theatre," says Hinch, "so she didn't feel deprived." But he signals a sense of frustration that "for 17 years she couldn't get auditions in the Australian film industry". Richard Walsh, a long-time friend and also the publisher of her 2007 memoir Much Love, Jac, says "she loves America because she feels as though she's valued there. She'd never complain [but] she's a long way from where she was five or six years ago."

Weaver tells me, "A lot of Americans say to me, fairly often, 'Why didn't you come here 12 years ago, 30, 40 years ago?' " But if she had come to the US earlier, she believes, there's a good chance she would have endured years of difficult rejection. "You can be really, really good and just not manage to get the break that you need. It can be very demoralising and make you very sad. I always thought that would have been my fate if I'd come here in my 30s or my 40s, whereas in Australia I was at the top of my game." Besides, she doesn't believe in regrets. "I wouldn't perhaps have been in Animal Kingdom, for a start, and that was a gift that gave the whole thing to me."

No one seriously anticipated the success the film went on to have. Michôd, Weaver and some of the other members of the cast paid their own way to Sundance for the screening, and they had already flown home, happy just to have been nominated for the Jury Prize, when the news came through that the film had won the coveted award. "It was something that had never been on my agenda, to be an Oscar nominee," Weaver says. But by the time it was announced, she had begun to be optimistic, since she'd been nominated for, and won, so many other awards for the role, including the prestigious US National Board of Review prize. At the time of the actual announcement, she'd grown tired of waiting and had fallen asleep in her hotel room at the Beverly Wilshire. She woke up when her phone started ringing; it was Hinch, saying, "You're in, you're in!" Shortly after that, she recalls, "the phone went insane".

The next Oscar nomination "was completely unexpected", however, since she hadn't been nominated for other prizes for Silver Linings Playbook. "I was hoping [co-stars] Jennifer Lawrence and Bradley Cooper would be nominated. Then my picture came up on the screen and they said my name and I just ran around the hotel room shouting 'F...!' ", she laughs. The recognition matters, she says. "It is a big deal. It's no good pretending it isn't. It's a basic human need, no matter what you do, to be told you've done a good job."

Now, as Brett Sheehy puts it, the 66-year-old "is fast becoming Hollywood's go-to girl for stellar, character-driven, truthful performance of roles for women over 60". He points out that not only is she "quite simply adorable", but that in a world where plastic surgery has become the norm, "Jacki's face is fully mobile and expressive, and can register and convey every emotion and nuance under the sun. The camera, and directors, love her because of this." Weaver points to a place on her chin she was thinking about having some work on and tells me, smiling, that her agent, Hildy Gottlieb at the powerhouse International Creative Management agency, told her firmly that she "mustn't do any changes to my face"; the only surgery she has had to change her appearance have been two operations to reduce her very ample breasts.

Hinch thinks Weaver has occasionally been underestimated because of her looks. "She's blonde, she's short, she had big boobs. Three strikes and you're out - you must be stupid." That is the usual perception, he believes. "And she's lived with that." Inside that tiny, gorgeous body is a fierce intellect and observant, analytic mind. She's a voracious reader and peppers conversation with perfectly rendered quotations from Oscar Wilde, J. D. Salinger and other writers. Discussing the recent adaptation of Charlotte Brontë's Jane Eyre starring Mia Wasikowska, Weaver mentions her disappointment that the script didn't include her favourite line, addressed to Jane by the blind Rochester in the final chapter. She lifts her chin and intones gleefully, "Why do you remain pertinaciously perched on my knee, when I have given you notice to quit?"

She has nothing of Jane's plainness, but shares with her a quality of captivating, controlled passion. Weaver's smallness of stature gives her presence somehow even more impact. Kate Mulvany recalls meeting Weaver in 2005 when they worked together onstage: despite her height, "she could fill a room just by walking into it. And yet there was no fanfare - she doesn't announce herself as so many other thespians do. Jac simply wandered in, her hair still damp from the shower, bare-faced, in comfy rehearsal clothes, smiled that high-wattage smile and said softly, 'Hello, I'm Jac.' "

It's the quality of what Alex Cole calls "quiet intensity"; Mulvany noticed it another time in "a massive, jam-packed pub in Fremantle, Western Australia" where it seemed as though she would be "swallowed by this seething mass of young, drunk, mostly male revellers. But then the masses parted and this kind of path appeared and Jac - like a tiny, blonde, giggling Moses - made her way through the ocean of blokes. A gaggle of young men suddenly appeared on each arm, accompanying her to her seat, asking if they could get her a drink. She didn't go looking for any of that. They just went to her. Moths to a shy but vibrant flame. And this happens everywhere."

If you try Googling her name, the helpful search engine will attempt to complete your search term with "Jacki Weaver husbands". She's been married five times, not including her relationship with producer John Walters, the father of her son Dylan, born when she was 22. And two of those marriages were to the same man, the so-called "Human Headline", Derryn Hinch. "I don't regret any of my chequered love life and my adventurous attitude to life," she says cheerfully.

In 2002, Weaver was cast in a production of the play Soulmates at the Sydney Opera House with a South African actor, Sean Taylor. When they were introduced to each other by the casting director one night at an Alan Bennett play, Taylor remembers, she smiled "the widest warmest smile and said, 'I hope you're not disappointed.' And I never have been." Reader, she married him, and they celebrated their 10th anniversary earlier this year.

When I meet them in LA - Taylor joins us later in the interview - they are both visibly relieved at having signed a lease on an apartment in West Hollywood, and the prospect of some hard-won time together. Taylor, 57, is tall and dapper, with a quick, open smile and long arms given to expansive gestures, a virgin mojito seemingly always in hand, and a strangely unplaceable accent - South African modified for the stage towards a patrician, British sound.

When he and Weaver arrive at the poolside lounge of the ultra-glamorous Sunset Tower Hotel, he's wearing a cerulean blue shirt that matches his eyes and also the sparkling swimming pool. The two of them chat with Weaver's manager about whether the producers of Reclaim, an upcoming film to be shot in Puerto Rico with Ryan Phillippe and John Cusack, will cover a plane ticket for Taylor as well, to allow the two of them to spend time together while she's doing the movie.

Gone are the days when Weaver could summon a private plane, when she and Hinch lived a famously extravagant lifestyle. Over dinner, she recounts to me a conversation earlier that day with Rebel Wilson: Rebel expressed her delight at being flown to some event in a Lear jet, and then showed something close to disbelief when Jacki disclosed, in her typically understated way, that she used to have regular access to a private plane. During a pilot's strike in the 1980s, Weaver recalls, she used the jet to fly from Melbourne to Sydney to work on a play she was appearing in.

There is a wistfulness when she talks about those days of luxury. What was it like, I ask, driving a Rolls-Royce as her everyday car (she and Hinch had one each for a while)? "It was terrific," she says, with sincere intensity.

The personal Learjet is no more, but that hasn't stopped Weaver taking flight to be with the one she loves. Kate Mulvany recalls a time when Weaver was on tour in Australia with the play Ruby's Last Dollar "and her hubby Sean was performing in South Africa. There was a three-day break between shows and Jac jumped on a plane to South Africa just to spend a few hours with Sean. That's Jac. Love comes above all things."

Tension between the demands of love and work has been a constant theme in their marriage, and has taken its toll. "We've had some very rocky times," she says. "I don't think it's good for any marriage, to be separated for long periods of time," she says. "I don't believe that absence makes the heart grow fonder. A couple of weeks here and there is fine, but when it gets into months and months ... there was one stretch when we were apart from each other for eight or nine months." They were in different cities in Australia, each working in a different play. "When he was in Brisbane I was in Adelaide, and when I was in Sydney he was in Perth." The exhausting demands of their performance schedules, with eight shows a week, made it "almost not worth it" to take the flight to see each other on their one day off.

Neither of them wants to go through those "enforced separations", Weaver explains, but "he can't turn down work". It's not just a matter of money or professional advancement. "He's got to work for his - well, for the reasons everyone does, for the soul." She speaks with sincere admiration of Taylor's talent and his reputation in South Africa, where "he's still a big star".

The two of them have acted in six plays together since their fateful meeting on Soulmates, including a celebrated production of Arthur Miller's Death of a Salesman in 2008. Weaver remembers that "we both got great reviews but his were slightly better". She proudly recites a phrase from one review, which noted that, "If Weaver is wonderful, Taylor is heavenly." "That's exactly the way it should have been," she says. "He was the best thing in the play. But I was the second best!"

There's a sensitivity on her part, almost a hyper-consciousness, about the way her spectacular recent success has overshadowed Taylor's own considerable achievements. "I was delighted," she says of that review when I talk with her a few days later, "and I was so relieved it wasn't the other way around." She laughs, but she's also serious. "It would have seemed so unfair for it to seem as though he was working in my shadow; he spends most of his life living in my shadow." Taylor seems comfortable with that, and shares Weaver's happy glee in their charmed circumstances.

Their new apartment is a modest place, with bare white walls and anonymous rented furniture, including a throne-like red leather armchair that seems to have been built for a giant. It's become necessary to have a base in LA because it has become the centre of Weaver's career, but her heart is very much still in Sydney, where her family lives. She remains close to her brother, barrister Rod Weaver, her son Dylan and his wife Makiko, and their two children, Taketora, 6, and Luli, 3.

She's immensely proud of having helped to deliver Luli, and is sad about being so far away from her grandchildren. Dylan is her only child, but, she says, she would have liked to have had more. In her memoir, she shares the story of a miscarriage that was the beginning of the end of her relationship with the late Richard Wherrett, founder of the Sydney Theatre Company and a man she has described as "the love of my life". But there were more miscarriages, she now admits - four altogether, all devastating.

Weaver's real home is her apartment in Darlinghurst, although she prefers to call it Kings Cross. "It sounds sleazier," she says with a cheeky smile. She shows me pictures on her phone of the living room, crowded with artwork and books. It was Wherrett's home; he left her the apartment when he died of liver cirrhosis in 2001, after a long struggle with HIV (she's quick to point out that he left her the mortgage as well). They had been separated for years by the time he became seriously ill and Jacki was in another relationship, but she moved in with Richard and nursed him with extraordinary devotion until his death.

It was a love affair that never really ended while Wherrett was alive, and he is in many ways an undiminished presence in her life even now. "There's photos of him everywhere" in the apartment, Weaver says, "and a beautiful mask that a wonderful artist made of him, and that's quite prominently displayed". There's also his ashes, which rest in her study "on a shelf wrapped up in a beautiful case of tulle". She accepts that other people might find it strange. "A lot of his friends used to say, 'When are we going to scatter Richard's ashes?' and I'd say, 'I can't let go of him yet.' They've given up asking. He's still there. I don't see why I should get rid of him." It's her way of dealing with his loss. "It's one subject that everyone makes judgements about," she says, "grief and people's modes of dealing with death. Everyone's different. People might think it's macabre, but to me it's a comfort." Her husband accepts the situation. "Well, I wouldn't care if Sean didn't like it," she explains, "but he doesn't mind."

One thing Weaver misses about Wherrett, she says, is his good advice. "When I'm trying to make decisions about work, I always think about how he would counsel me." If she was faced with a dilemma over which role to choose, "he'd encourage me to do the one that was the most challenging, the most dangerous, the most difficult, instead of the safe way. He'd say, 'Don't be afraid, don't be scared, don't be nervous, have courage.' "

"All her life she's been a risk-taker," Richard Walsh points out, with a "sense of adventure" that has made her unafraid of "edgy" work. Brett Sheehy agrees. "She is utterly fearless and will try anything." The success she's enjoying now shouldn't be considered a matter of luck, Walsh cautions; rather, he sees it as a result of remaining open, and taking a chance on interesting projects and untested directors - like Animal Kingdom. "Sooner or later, if you're generous like that, good things do happen," he says.

Wherrett is not the only ex-lover who remains part of Weaver's life. She still speaks every day with Hinch, although their tumultuous marriages ended years ago, and when I talk with her on the phone, she explains that she will "always love him. That's not to diminish anything I feel for my husband." At this, sounds of mock protest are audible from Taylor, who is on his way out to the pool. "It's more than a close friendship," she says, but "it's not a romantic connection".

What will the next chapter be? Alex Cole foresees that Weaver will move from the mostly independent film work she's doing now to more commercial movies. Weaver has a clear idea about what she wants: "To be the protagonist." She's played supporting roles for a while, but would like to be at the centre of the story. When I ask Cole where he sees her in five years, he says he imagines her in a suit, playing the CIA's director, "with a red phone in front of her and a room of 25 men in military uniforms, very manly men at the Pentagon and her, all four-foot-eleven, commanding that room where you won't hear a pin drop, telling them to deploy the Seventh Fleet ..."

It's not hard to imagine at all, considering how much she does seem to have the world at her command.