Thin privilege is Dean Winchester’s behavior in the Supernatural episode Appointment in Samarra (episode 11, season 6) in which Dean takes Death’s place for a day. The first two people he had to kill were presented as “no great tragedy” because the first one was a homicidal criminal threatening to kill a child, and the second was a fat man.

The fat man eats a pizza, and dies of a heart attack. When he asks why he had to die Dean says, “Maybe it was the extra cheese.” And then he proceeds to ask the guy where he got the pizza because it looks good. So when a fat guy eats a pizza, he deserves to die, but it’s perfectly okay for the skinny guy to eat the exact same thing.

So the second man’s sin deserving of death wasn’t his behavior - his diet. It was clearly his existence as a fat person that was deemed morally wrong. Thin people can engage in the same behaviors without punishment, but eating while fat is a sin on par with threatening to murder a child.