I suspect part of it is they think their fat children make them look normal - it's a genetic thing, it runs in the family - it's a glandular disorder etc. As an acquaintance, a PT instructor used to say - no one over came out of Belsen fat because of a glandular disorder.
"Glands" is what my tubby poorer friends would say when I was young 35 years ago. The difference between them and my wealthy friend's candy confiscating mother is when I went to their house, we'd ride atvs and play Nintendo and eat bags of cookies. It was an issue of habit there. Back then, eating mostly processed food was uncommon, but that's what they did in the house. All of the kids were fat. The mother was thin, I didn't see her eating much.