Green’s Dictionary of Slang

corpulent, obese.

1890–1904		Farmer & Henley Sl. and Its Analogues.
1902		E. Townsend Chimmie Fadden and Mr Paul 82: Miss Fannie would sneak to de stables and stuff it wit steak till it was as poddy as a jug.
1915		S. Ford Shorty McCabe on the Job 85: All we had on the slate was a couple of poddy old parties who’d be workin’ away at the apparatus.