The belly. Some think paunch was the original name of that facetious prince of puppets, now called Mr. Punch, as he is always represented with a very prominent belly: though the common opinion is, that both the name and character were taken from a celebrated Italian comedian, called Polichenello.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Paum * PawNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes