Remember, in ancient society, obesity represented wealth and prosperity; the “Good luck Buddha” or “Hotei” of Japanese and Chinese culture was heavy to represent good health and prosperity, a mere symbolism, if you will, except it was trying to show prosperity and health of the mind.
Religious beliefs adjust deities to best serve their own agendas. No where does it say that God is a bearded man in a robe. Religion made it so. As a matter of fact, God was originally worshiped as a woman called Goddess, until religion changed God into a man.
He is portrayed that way because, in the ancient world, it was considered a sign of prosperity to be fat. Being fat meant that you had wealth, could eat well and that you had plenty of resources. Thinness was a sign of poverty and ill fortune. That is why Buddha always has a nice, round belly.
The ‘fat Buddha” is actual Hotei or Budai–a pre-Buddhist god who was adopted into Buddhism
Buddha said, “Make no image of me”
The fat buddha, I believe was originally meant to refer a buddha in general and not, the Buddha. In India, any enlightened being is called a buddha (self-realized, enlightened, etc.). Siddhartha was known as the Buddha for being far advanced than the usual buddha.
Technically, Krshna, Jesus, Mohammad, Moses, etc, would also be considered buddhas.