Sigourney Weaver was born Susan Alexandra Weaver in Leroy Hospital in Manhattan, New York City. Her father, TV producer Sylvester L. Weaver Jr., originally wanted to name her Flavia, because of his passion for Roman history (he had already named her elder brother Trajan). Her mother, Elizabeth Inglis (née Desiree Mary Lucy Hawkins), was an English actress who had sacrificed her career for a family. Sigourney grew up in a virtual bubble of guiltless bliss, being taken care of by nannies and maids. By 1959, the Weavers had resided in 30 different households. In 1961, Sigourney began attending the Brearley Girls Academy, but her mother moved her to another New York private school, Chapin. Sigourney was quite rather taller than most of her other classmates (at age 13, she was already 5' 10"), resulting in her constantly being laughed at and picked on; in order to gain their acceptance, she took on the role of class clown.

In 1962, her family moved to San Francisco briefly, an unpleasant experience for her. Later, they moved back east to Connecticut, where she became a student at the Ethel Walker School, facing the same problems as before. In 1963, she changed her name to "Sigourney", after the character Sigourney Howard in F. Scott Fitzgerald's "The Great Gatsby" (her own birth name, Susan, was in honor of her mother's best friend, explorer Susan Pretzlik). Sigourney had already starred in a school drama production of "A Midsummer Night's Dream", and, in 1965, she worked during the summer with a stock troupe, performing in "A Streetcar Named Desire" and "You Can't Take It With You" (she did not star in the latter because she was taller than the lead actor). After graduating from school in 1967, she spent some months in a kibbutz in Israel. At that time, she became engaged to reporter Aaron Latham, but they soon separated.

In 1969, Sigourney enrolled in Stanford University, majoring in English Literature. She also participated in school plays, especially Japanese Noh plays. By that time, she was living in a tree house, alongside a male friend, dressed in elf-like clothes! After completing her studies in 1971, she applied for the Yale School of Drama in New Haven. Despite appearing at the audition reading a Bertolt Brecht speech and wearing a rope-like belt, she was accepted by the school but her professors rejected her, because of her height, and kept typecasting her as prostitutes and old women (whereas classmate Meryl Streep was treated almost reverently). However, in 1973, while making her theatrical debut with "Watergate Classics", she met up with a team of playwrights and actors and began hanging around with them, resulting in long-term friendships with Christopher Durang, Kate McGregor-Stewart and Albert Innaurato.

In 1974, she starred in such plays as Aristophanes' "Frogs" and Durang's "The Nature and Purpose of the Universe" and "Daryl and Carol and Kenny and Jenny", as "Jenny". After finishing her studies that year, she began seriously pursuing a stage career, but her height kept being a hindrance. However, she continued working on stage with Durang (in "Titanic" [1975]) and Innaurato (in "Gemini" [1976]). Other 1970s stage works included "Marco Polo Sing a Song", "The Animal Kingdom", "A Flea in Her Ear", "The Constant Husband", "Conjuring an Event" and others. However, the one that really got her noticed was "Das Lusitania Songspiel", a play she co-wrote with Durang and in which she starred for two seasons, from 1979 to 1981. She was also up for a Drama Desk Award for it. During the mid-1970s, she appeared in several TV spots and even starred as Avis Ryan on the soap opera Somerset (1970).