Above is 'The Fat Men’ Scene from the film ‘Wait and See’ made at the Nettlefield Studios, Walton on Thames in 1928, featuring London’s "Thirty Fat Men." My guess is that the "Thirty Fat Men" was a fat man's club, which used to be pretty common in the late 19th and even up into the 20th century.
Clubmen circa 1900 have a "Fat Man's Contest
Not just for the turn of the century: Sailors of the USS Irex started one in 1953
ETA: Read about a Fat Man's Ball from earlier.