After college, Weinberg worked as a real estate appraiser in the inheritance tax section of the State Auditor General's office. In 1939, he was one of three Democrats nominated for City Council in the 1st district, but Republicans took all three available spots in a close election. Three years later, he was elected Democratic ward leader of the 39th ward. Weinberg was named an assistant state treasurer in 1943. He served as a delegate to the 1952 Democratic National Convention.