The sensation of having eaten so much one feels as if they are a 'balloon dog', a dog shaped baloon-animal, the type often made by a clown for a child; under extreme pressure and ready to explode any second.
"Hey sorry about that, we ate a couple seafood platters and got completely balloon dogged before we got here. I shouldn't have fed her those last five drinks. That will need to be steam cleaned."
"No desert thanks, I am totally fucking balloon dogged after eating that family of hippopotami."