Zweig started buying stocks as a teenager, reputedly purchasing his first stock at age 13 and from that point on vowing to become a millionaire. Following high school, he earned degrees from three of the nation's leading business schools, including a BSE from the Wharton School of the University of Pennsylvania in 1964, an MBA degree from the University of Miami in 1967, and a Ph.D. in finance from Michigan State University in 1969. He later taught finance at Iona College and Baruch College.

He started his career in the 1970s as an investment newsletter writer and contributed numerous articles to Barron's Magazine. He went on to become a successful and influential investment advisor on Wall Street, known for his exhaustive data studies. In 1986, Zweig authored the book Winning on Wall Street (ISBN 0-446-52533-2). In it, he called Jesse Livermore one of his heroes and "one of the most fabulous traders of all time," recommending that people read the 1923 Edwin Lefèvre book *Reminiscences of a Stock Operator.

Zweig appeared regularly on PBS television's Wall $treet Week with Louis Rukeyser and in 1992 he was voted into the program's Hall of Fame. It was on that very program that he stated on October 16, 1987 he was deeply worried and did not like what he saw in the stock market, three days before the 1987 stock market crash. He is currently the Chairman of Zweig-DiMenna Associates, Inc. He is also featured in John Reese's recent book, The Guru Investor: How to Beat the Market Using History's Best Investment Strategies.