My teen rapidly put on weight once she got old enough to start buying her own food and eating out. You reach a point where things are no longer in your hands. Now she is at uni she is realising that she needs to lose weight and has taken up running, walking and football. I also give her healthy suggestions for lunches instead of pizza!
I think the main causes of obese children are:
portion sizes - feeding small children a portion suitable for an adult (dp was very guilty of this with his youngest and was surprised that I suggested cutting it down a bit)
obesity blindness - literally not seeing that your dc are overweight (dp also guilty of this and it's only now looking back at photos of his youngest that he realises how massively overweight she was aged 9 and that wearing adult sized clothes to fit her wasn't great)
lack of education - I mean properly learning to cook. I don't mean knowing about nutrition, I mean learning to cook everything from scratch.
I really think there is a huge need for some sort of buddy system whereby the older generation with some free time can buddy up with someone younger with dc to help them learn to cook and shop healthily and efficiently. Not patronising, just passing on the knowledge.
One last thing is exercise. You often find people saying their dc exercises loads - they do a dance class/play football once a week and are always out on their bike. That's not really loads.
My youngest does 2 hours swimming, 1 hour athletics, 1 hour rounders, 1 hour cricket, about 4 hours walking plus two hours PE lessons every week. Plus going out on her bike. She is naturally slim anyway but would easily put on weight around her tummy if she wasn't so active. She snacks on tomatoes, grapes and carrots (she is the oddest child I know) as well as the odd packet of crisps or brownie.
No food is a bad food in this house. However, I will say only one small punnet of grapes, only one packet of crisps, only one brownie etc. Because she needs to learn to eat food she loves but in moderation.
Biggest treat for her is a punnet of raspberries.