My DS is 11 and is heavier than I'm comfortable with. He has ASD which manifests itself in a number of ways but one is that he doesn't make great food choices (doesn't eat vegetables and only a few fruits). I can control what he eats to a certain extent at home, but he can eat what he wants at school. The rest of us are all slim, eat quite good diets, and exercise regularly, so it is quite difficult trying to keep things balanced at home for him.
In terms of exercise, he's not got fantastic coordination, and although claims to enjoy rugby etc at school, I can't imagine he's actually doing much (his grade in his last report confirms that!). Other things he does:
Trampolining club at school weekly (reality is probably not much time in the trampoline)
Tennis club at school weekly
Tennis club on a Saturday weekly
PE/games at school for 3 lessons I think.
We're out of the house for long hours in the week, and have various commitments so would struggle to fit in much else after school. Weekends they have homework, and I think they need some down time.
We try and do something active as a family most weekends - at the moment they're training for a 5k next month, so we have Sunday Runday where we all go out together to jog. We often will go for walks (not been great weather for this lately...). DS is bike phobic, so bike rides are rare and very very stressful initially, although quite enjoyable once he realises he's not going to fall off.
He loves swimming (not lengths though, just bobbing around), likes Crazy Climb (but it's half an hour away and is a big chunk of time required we don't t often have). In school holidays he comes with me to see my PT fortnightly and joins in with most of it.
But he's just not one of those boys who runs around a lot, never has been. Always much happier sitting still with a book (or whenever possible, a screen). It's not easy, and there's a part of me that hopes he'll just grow very tall and be able to carry off the extra pounds (DH is v tall so quite likely to follow suit).
So, do what you can together, make exercise a normal part of your life as well as family life (so he sees you modelling the good behaviour), and try to change small things in your life (walk when possible etc). But ultimately, they have to choose their own path, and you can only do your best.