[1] After attending Roslyn High School,[2] Weinstein obtained a bachelor's degree at the Massachusetts Institute of Technology in 1964.

His teachers included, among others, James Munkres, Gian-Carlo Rota, Irving Segal, and, for the first senior course of differential geometry, Sigurður Helgason.

[12] In 1974 he worked with Jerrold Marsden on the theory of reduction for mechanical systems with symmetries, introducing the famous Marsden–Weinstein quotient.

[13] In 1978 he formulated a celebrated conjecture on the existence of periodic orbits,[14] which has been later proved in several particular cases and has led to many new developments in symplectic and contact geometry.

[2][11] Building on the work of André Lichnerowicz, in a 1983 foundational paper[17] Weinstein proved many results which laid the ground for the development of modern Poisson geometry.