I'm looking for examples of jokes poking fun at fat people in ancient Greek comedies. So far from my research I have been unable to find anything.
Were there any such jokes or was being overweight not considered a source of humour?
In "old comedy," aka 5th century Aristophanic comedy, there are a lot of visual gags that fit your description. Much of the Greek comic male costume often included prosthetics that gave the actor a large belly, big butt, and (often) outsized phallus. See here and here for examples from vase painting. So, when, for example, Dionysus is spanked in Frogs, the audience is seeing his (probably) bare, big butt get hit over and over while he pees himself.
There's also a lot of fart jokes that would probably be accentuated by the actor showing off their large posterior, and so forth...