> I think fat people have something wrong with them where the whole process of eat food -> feel sated is off.
This isn't something that's wrong with fat people, it's something wrong with the food environment they're in. 75 years ago your idea would have some intrinsic plausibility, as only a very small number of people had obesity. Now, in the United States, we're at a point where ~40% of adults have obesity. The explanation almost certainly lies with changes in the food environment, instead of with a huge portion of people catching an unknown disease that causes them to not know how much they're eating.
That's because in fact we do know about changes to food environment that could cause this. Since roughly the 1970s we've switched to foods that are more calorie-dense and less nutritious because they have become cheaper to produce. The relative cost of soft drinks and other sugary goods has increased much less than the cost of fresh vegetables, and in fact the industry has higher profits on these foods. I bought two liters of sugary soda for $1 the other day, that's a common offer at a grocery store near me.
If you drill down to how this is being accomplished, you'll notice that the rates of corn and soy production per person have vastly increased over the last 50 years. That's not because people are eating more tofu (which would be healthy), it's because (a) they're both used as additives or sweeteners (corn syrup), and (b) they're used as feed for animals who get turned into cheap meat at fast food restaurants. The US heavily subsidizes these crops - in fact they make up close to half of US farm land. As a result, the same (genetic) individual would almost certainly experience a much worse food environment today than in 1960.
People who aren't affected by this are those who are either (a) genetically blessed, and would hardly gain weight in any environment, or (b) are socially blessed, in that they are wealthier, live in places with a strong culture of exercise, and/or have easy access to nutritious fresh vegetables.