Transference

Imagine you are ten years old. Imagine the school nurse comes in, looks at all the kids in your class. Imagine you get a letter a few weeks later saying you should stay after school because you are a fat kid and you need to engage in some non-competitive physical activity three times a week to ward off obesity.
Good intentions. Bad plan.
Kids are mean. They're adults who haven't learned how to tame their base instincts and they love to find the weaknesses of other people. Kids will find out that Joey's going to the fat kid afterschool program and tease the everloving bejesus out of him.
I'm not saying that childhood obesity isn't a problem, or that a kid should just be left in front of the TV with bags of chips. I just think it's a bit unrealistic to expect kids to be okay with being sent to an afterschool program that their nasty peers will find out about and humiliate them for. I mean, just walking around in a sports bra when I was twelve for the scoliosis test was traumatizing enough for me, and I wasn't that overweight. I can't imagine hearing, "Hey, have fun at the fat camp today" at that age. So you'll have fit kids who still feel bad about themselves because their peers will know it's a sore spot.
I think that schools need to include all the kids in the healthy eating and physcial activity plan. Back in the day, it was called "phys ed." Even kids who are skinny can still eat shitty foods and not get enough exercise, but they're lucky enough to have the metabolism for it. Keep the gym and recess time for kids in the school day, and work on the eating in health class. Don't put the fat kids on the metaphorical short bus.