His family is Jewish, and his maternal grandparents immigrated from Poland. He grew up with his younger brother, Bob, in a housing co-op named Electchester in New York City. Weinstein graduated from John Bowne High School and attended the State University of New York at Buffalo.

Weinstein, his brother Bob, and Corky Burger independently produced rock concerts as Harvey & Corky Productions in Buffalo through most of the 1970s. Harvey & Corky Productions brought top acts to Buffalo, including Frank Sinatra, The Who, Jackson Browne, and the Rolling Stones. Dandes, followed him to Buffalo and has described Weinstein as 'aggressive' and 'consumed' in matters of business.