Weissman was working on a project on fluorescent energy transfer, which later led to some rare-earth lasers, at the University of California at Berkeley when he was asked to join the Manhattan Project developing atomic weapons in 1943. He was among a group who asked unsuccessfully that the bomb not be dropped on civilian targets.
After his Los Alamos stint, Weissman went to the Washington University in St. Louis in 1946 becoming a full professor in 1955. At Washington University, Weissman worked with others developing the use of electron spin resonance. He was one of the first, probably in parallel with Clyde Hutchison, to measure the hyperfine splitting of the ESR line caused by the interaction with nuclear spins. This hyperfine splitting is the main source of the sensitivity of ESR to the chemical environment of the electron, and hence it underlies the broad applications of ESR in chemistry. Much of his work concerned the way this interaction term behaves as molecules tumble around in solution or undergo chemical reactions. He also investigated the special non-equilibrium ESR effects which are found as reactions take place.
Weissman was a member of the United States National Academy of Sciences. Weissman retired from Washington University in 1980 and died in June 2007.