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Weiss learned clarinet, violin, and tuba when young, and switched to bass in his teens. He moved to New York City around 1931 and worked in the following decade with Louis Prima, Bunny Berigan, Wingy Manone, Artie Shaw, Tommy Dorsey, Charlie Barnet, and Adrian Rollini. He was with Benny Goodman from 1941–45, then played in the second half of the 1940s and the early 1950s with Muggsy Spanier, Pee Wee Russell, Cozy Cole, Bud Freeman, Duke Ellington, and Eddie Condon. He quit full-time performing in the mid-1950s and in 1968 was an executive of the musicians' union in Los Angeles.