Weinstein was born in New York. After serving in the navy during World War II, he studied at Hunter College and Harvard.

He first collaborated with Bolcom on an antiwar satire titled Dynamite Tonight, which premiered in 1964 at New York's Actor's Studio. His play The Red Eye of Love played off-Broadway in 1961, and his adaptation of Ovid's Metamorphoses was produced on Broadway in 1971.

Weinstein also collaborated with painter Larry Rivers on Rivers' What Did I Do? The Unathorized Autobiography, and taught at Yale and Columbia. But he will be best remembered for the trilogy of operas he created with Bolcom.

Weinstein wrote the libretto for McTeague, based on the novel by Frank Norris, with filmmaker Robert Altman, who also directed. It debuted at the Lyric Opera of Chicago in 1992, with a cast that included Ben Heppner and Catherine Malfitano.

A View From the Bridge was based on Arthur Miller's play; Weinstein collaborated with Miller on the libretto. It opened at the Lyric Opera in 1999 and was revived at Metropolitan Opera in 2002. Malfitano, Kim Josephson, and Gregory starred.

The Wedding, which opened at the Lyric to rave reviews in December 2004, was based on Altman's 1978 film, and the filmmaker again directed and collaborated with Weinstein on the libretto. Lauren Flanigan, Anna Christy, Malfitano, and Mark Delevan headed the ensemble cast.