Weaver died November 26 at home in Manhattan, The New York Times reported.
Weaver received his Tony in 1970 for his performance as strict Catholic boarding school teacher Jerome Malley in Robert Marasco's long-running thriller Child's Play.
The 6-foot-3 Pittsburgh native made his Broadway debut in 1955's "The Chalk Garden," for which he landed his first Tony nomination. He also played Sherlock Holmes in the 1965 musical "Baker Street" and appeared in such productions as the 1962 musical "All-American," Alan Ayckbourn’s 1974 comedy "Absurd Person Singular" and Lanford Wilson's "Angels Fall" in 1982.
Weaver was inducted into the Theatre Hall of Fame in 2010.
In his movie debut, Weaver portrayed a rattled Air Force colonel facing a nuclear crisis in Sidney Lumet's classic Fail-Safe (1964), and he was an evil mastermind bent on using trained dolphins to attack the president in Mike Nichols' The Day of the Dolphin (1973).
His film résumé also included The Maltese Bippy (1969), Marathon Man (1976), Demon Seed (1977), Black Sunday (1977), The Big Fix (1978), a segment of Creepshow (1982), Lumet's Power (1986) and the 1999 remake of The Thomas Crown Affair.
In the 1990s he appeared as Hugo Marick in ABC daytime soap opera All My Children.
More recently, Weaver appeared in the 2013 HBO telefilm Muhammad Ali's Greatest Fight and in the features The Cobbler (2015) and The Congressman (2016).
Weaver worked often in television, earning an Emmy nomination in 1978 for portraying a Jewish doctor sent to Auschwitz in the NBC miniseries Holocaust.
He starred in two episodes of the original The Twilight Zone, including 1960's "Third From the Sun," in which he played a scientist who tries to hijack a rocket to get him and his family off Earth as nuclear war beckons.
Weaver also appeared on the small screen on Playhouse 90, The Defenders, Gunsmoke, Dan August, Hunter, Mannix, Falcon Crest, Law & Order and dozens of other shows. Recently, he narrated specials for the History channel.
His sister was Mary Weaver Dodson, a four-time Emmy-nominated art director known for her work on Murder, She Wrote. She died in February.