Instead of attacking fat people (who are one of the last groups within society that people are allowed to openly bitch about), it might be better to attack the food industry which fills products with addictive chemicals and other crap.
Money may well be an issue - the cheaper foods are the ones filled with shit.
I am currently on a diet and everywhere I look, I am surrounded by high fat, high salt, high sugar crap. It's hard enough for me to resist them, let alone kids. If they weren't everywhere, then society would find it easier to be healthier.
Yes, parents are ultimately responsible for what they feed their kids, but firstly, a lot of people don't actually realise just how unhealthy or high calorie some food actually is. A sandwich from a supermarket can appear healthy, but have 500 calories in. Maybe this mum isn't feeding her kids wall to wall burgers, just normal food which has been processed in a way that isn't made completely obvious at the outset. I was surprised by how many calories some vegetarian products have, as I had always thought of vegetarian food as healthy .and some of it really isn't
Secondly, one of those children is a teenager - they have access to their own money at that age and the freedom to play out with their friends. I think it is impossible to control their diet entirely at that point.
Maybe there are underlying conditions or maybe she has kids who are resisting all attempts to get them exercising (was a serious exercise avoider myself as a child, although I was skinny) and she is trying not to make it a chore but something they actually want to do.
I think this is a horrible OP and it's a cheap shot to attack overweight people when most things in society conspire to keep them that way. I'd like to see free, easily available sports clubs for all kids in all areas and free gym memberships for teenagers and decent canteen food in Secondary schools, instead of garlic bread and chips and chocolate vending machines. If we had better facilities, available to all, then perhaps this woman's kids wouldn't be fat.