It's kinda tied to some of the things that I like. There are three things that I am into: fatfurs, big paws, and thick stretchy limbs usually made up of a connection spherical body parts, usually a neck or an elephant trunk. That last one is a little unusual, so I guess you could count that.
But it's usually not enough for a character to have a big belly/big feet/big stretchy neck or nose. What all we've completes these characters for me is how much of a total ham they are. I don't know why, but when these characters are boasting about very mundane things about their body that really don't make them that powerful as if they are the most destructive forces around, that makes them feel more special and Charming for me. Add some bonus points if the character has Minions that are capable of doing magic or use weapons, But they are so powerful that they only need to use their belly/feet/thick stretchy limb to beat you. Even more bonus points if they have such a huge ego that they feel the need to rap about themselves.
As for why I like those thick stretchy limbs so much, I have a feeling Is it started with the mammoth boss from Super Adventure Island 2.
This really is a stupid boss. It starts out pretty promising with the boss being encased in ice and throwing snowballs, but once you destroy the ice-barrier, all it does from there on out is flail about its trunk and charge at you. ... but a few things makes this boss enjoyable. The boss has this very goofy and somewhat Charming in look on his face, and the Simplicity of his moves both makes it easier to ham him up. His trunk also moves in a somewhat hypnotic way, so that is kind of hard to explain. Lastly, it is kind of fun whacking away at his trunk to make it shrink. I find myself trying to fight this guy with my bare fists, continuously punching his trunk and his eyes and then hoping I mess up enough times for him to beat me because I just like the character too much to actually want to beat him.