I was just thinking "hating on fatties" was one of the last "acceptable" prejudices. While you can't bully the fat kid in school by calling him names, we, as a people, still look down on fat people as lazy or undisciplined. So, to me, we already think "Dude can't even push away from the plate for his health. How in the hell can he run a country?"
And your "perhaps fat people are too lazy to run for public office in the first place" sort of summarizes what we think of fatties.