Weaver won the Tony Award for Best Actor in a Play and the Drama Desk Award for Outstanding Performance for the Broadway play "Child's Play" (1970). His other Broadway credits included "The Chalk Garden" (Tony nomination and Theatre World Award win), "All American", "Baker Street", "Absurd Person Singular", "Love Letters", and "The Crucible". He appeared in the off-Broadway play "Burnt Piano" for the HB Playwrights Theatre, and with Uta Hagen in a television adaptation of Norman Corwin's play "The World of Carl Sandburg".