Algernon Moncrieff from Oscar Wilde's play The Importance of Being Earnest. In his Establishing Character Moment, he's seen eating the cucumber sandwiches his butler left for his aunt. In fact, it's Lampshaded by the protagonist Jack Worthing on more than one occasion — including his very first line!
Fat Characters
Little Red Riding Hood from Into the Woods is described as being rather plump, and when she's at the Baker's she nearly cleans him out of his bread and sweets. She says it's for her grandmother, but she ends up eating all of the sweets along the way as well as half of a loaf of bread. When she gets eaten by the wolf later on, who just at Granny as well, the narrator laughs and comments that it was a full day of eating for both.
Falstaff from Shakespeare's Henry IV plays. In addition to being a drunkard, he runs up quite the food bill at Mistress Quickly's.
The titular protagonist from Ubu Roi attends a banquet his wife cooked up for their various co-conspirators including such delicacies as "tarty-farts", "turkey bum", and "balogna soup". Upon realizing that his wife is going to give away all that lovely food, Ubu chases the others out with a toilet brush so he can finish it himself.
