Alice Waters started this program in Berkeley, CA
I was a very heavy kid, at a time when there were very few heavy kids around (and I'm 46, so much has changed in a few decades). I see kids at my gym (a Y), and while I think some of the exercise programs and camps are great, it seems to me the gym, in general and for longer periods of time, isn't geared so much to a kid's temperament and lifestyle. The kids hang around and get bored and act goofy. It can be disruptive for adults on tight schedules who can't use the machines (while the kids are lounging, unsupervised).
I can't say I know what the answer is, teaching/allowing kids to be more active in regular and/or organized sports/activities. With families if possible. I hear you about feeling self conscious. Maybe people in general need to move beyond their shame and embarrassment, and adults need to help kids with this, to move and act and exist in the world no matter what size we are.