The lack of access to outdoor space doesn't explain the rise in childhood obesity. I used to work in a rural primary school where most of the DC lived within easy walking distance. Less than 200m from the school gate there was public open space, with a footpath leading out of it into the countryside. Within between15 minutes walk and 15 minutes drive (and the vast majority of school families had cars) there was river swimming, two enormous playing fields, a wildlife reserve, open-access woodland, National Trust land... All you might need beyond what you'd have anyway (sunscreen, trainers, trousers, t-shirt) would be a swimsuit and a towel.
And still... out of 30 DC in a class, at least a quarter to a third would be noticeably overweight - all the way from 'excess puppy fat' to 'clinically obese'. One of those DC had a DM who was a gym instructor. Most of the overweight DC did not have SEN of any kind.
Life has always been tough for a lot of families - it was tough for mine for my entire adolescence, money was tight, DM was busy - but when I was a kid, fat DC were a rarity. You didn't get to be picky unless you would literally starve for a week rather than eat what was in front of you, because the same food would come around tomorrow, with no option for anything else except perhaps an apple. IME truly picky eaters are absolute rakes - not to say that some picky eaters aren't overweight, but the ones I've known were skinny little things.
The issue is diet: what's in it, how often people eat, and how much they eat.
UPFs - easily available, relatively cheap, highly palatable, fat- or sugar-heavy, but not sustaining. Eat a large cookie or a piece of cake for breakfast (I knew at least one DC who did this), and you'll be hungry again an hour later. Eat a bowl of yoghurt and a banana and not be hungry again until lunchtime. A lot of lunchboxes were packed with UPFs, often aggressively marketed as 'children's foods'.
Snacking - sweets brought in to celebrate birthdays (which is a nice thing to do, but it normalises the culture of snacking), a snack at break, a snack on the way home from school.
How much - ever-increasing portion sizes (and, see above, unhealthy foods being relatively cheap, and people snacking constantly)
....and we end up here.
I could be thinner. I know how hard it is to stop snacking and lose weight. I know how easy it often is to distract an upset DC with a biscuit. This is a massively complex issue to tackle, and it is everyone's concern, if we care about public health, the well-being of individuals and the issues facing the NHS.