If a parent has weight issues they find hard to get under control, they're probably underestimating the amount they eat.
You hear larger people saying all the time that they hardly eat anything compared with 'x' who's thin. They clearly don't link the fact that the 'little' they think they eat is actually a substantial amount. Also, it's often the wrong kind of food.
SIL, for example, has been overweight since childhood. She eats things like pork pies, sausage rolls, cheese, white bread, etc on a regular basis. Because she doesn't eat lots of puddings or sweet things, she thinks she should be thin. It's just her warped perceptions.
Take that to a parent and they think they're eating little or not eating the wrong things, when actually they're taking in way too many calories, and they'll feed their kids in the same way. It's not them being cruel. It's them not knowing any better.
A few too many calories taken in regularly over a number of years will soon lead to major weight issues. Then you've got to start saying no to your kids. And we all know parents who won't say no to their kids for anything, let alone something as emotionally fired as food.
I don't know if there's an easy answer to this. Clearly, at a certain stage, when obesity becomes a health issue for a child the state has to intervene in some way. They need to educate the children and the parents so that BOTH are aware of the implications of their diets/lifestyles.