Jon is a massive Elvis fan. He referred to Stephanie as Elvis before she was born because they didn’t want to know the gender before birth.

When he says “fat Elvis,” I believe he is referring to the shambles the man’s life was in before he died. His “people” were giving him uppers to perform and downers to sleep. No one cared enough about the human to get him on the track to being healthy. He was milked for every dollar he could make other people. His marriage failed. He had few years with his child. The “fat Elvis” is the mental image of the mess his life was when he died.