Hi, PhD in biology here: you're wrong!

Not only are there direct genetic factors but also indirect ones (e.g. causing decreased thyroid activity, or depression which is often treated with drugs that make you gain weight), epigenetic factors, and so on.

Also you're wrong about “fat logic”: both your gut bacteria and they fat itself emit hormones that make you eat more fattening stuff. It's literally harder for a fat person to eat less.

Biology is complicated, so there's a genetic factor in almost any behavior. Of course even more so for someone survival critical like hunger.

Hope you learned something.