Weaver admitted that she had a difficult time at Yale. She was not fond of the shows at Yale Repertory Theatre, and had little luck getting lead roles in school productions. Some acting teachers referred to her as "talentless" and advised her to stick to comedy. Weaver credited her friends such as Christopher Durang, who kept hiring her for his plays, as well as her time at the Yale Cabaret, as crucial in helping her pull through. She graduated from Yale with a Master of Fine Arts in 1974. Before leaving Yale, she performed in the first production of the Stephen Sondheim musical "The Frogs", alongside Larry Blyden and fellow students Meryl Streep and Durang.