From PEOPLE Magazine Click to enlarge
Let's get this out of the way: Yes, in her new USA series Political Animals, Sigourney Weaver plays a former First Lady who runs for her party's presidential nomination, loses and becomes Secretary of State. Yes, that does sound like a certain public figure. But truly, says Weaver-who in person is as warm and quick to laugh as her public image is steely and Amazonian-she's not playing Hillary Clinton. In fact, she's sorry to report that they've never met. "I'm a great admirer of Mrs. Clinton, and it's been fascinating to read about her," says Weaver. "And I'm glad she's in the news so much because it's like, 'Wow! Yeah! My sista!'"

The pair do have longevity and toughness in common. After shooting to fame in the 1979 blockbuster Alien, Weaver, 62, has been a sought-after actress for decades, appearing in movies that include Ghostbusters, Avatar, Gorillas in the Mist and Working Girl. "I was told at [Yale] drama school that I wouldn't be successful because they thought I had no talent," she says. "So I'm amazed."

But Susan Alexandra Weaver didn't exactly grow up far from the spotlight: Her father, Pat, created the Today show, and she grew up in New York City, inspired by her parents' actor friends such as Hume Cronyn and Jessica Tandy. "They were still working at 70 and 80," she says. "I thought, 'That's cool.' " Her parents did too and, after Stanford, supported her dream (as a teenager she snagged the name Sigourney from a character in The Great Gatsby). "I was [nearly 6 ft.] tall when I was 11, so I was a freak, and I'm grateful that I had parents who encouraged me to be myself," says Weaver, whose first film was 1977's Annie Hall. "I don't know how else one can be!"

She's encouraging the same spirit in her only child, Charlotte, 22, whom she and her husband, Jim Simpson (founder and artistic director of Manhattan's Flea Theater), had a few years after they wed in 1984. "We've never really had a talk about any of [my career] stuff," says Weaver of their relationship. "I think she prefers to think of me as 'just my mother.'"

When she's not working-she'll star in the play Vanya and Sonia and Masha and Spike in New York City later this year-Weaver lives a quiet life in Manhattan with Simpson, going for walks and eating home as often as possible. "I'm always encouraging my husband to cook because he's quite good, and I clean up!" she says. "I cook roast chicken and lamb chops, but he's good at the yummy stuff." To maintain her striking good looks, she practices karate-"it's so good for your mind and body"-and she admits to being "slightly anal" about protecting her skin. Botox? She tried it once for a role. "Never again," she says. "My husband and daughter made so much fun of me, I thought, 'It's not worth it to go home and deal with this!' " Kidding aside, Weaver has no regrets-about anything. "It's a great business," she says. "And I've been very lucky."