I was an introverted kid who really had no interest in athletics, even though I was never really overweight. I was really uncoordinated, esp. with eye-hand coordination, so even if I could run okay, I wasn't going to be good at sports. Rather than be the guy that makes his team lose and brings shame and scorn upon himself, I chose to never be on an organized team since t-ball in kindergarten. (And I was horrible, horrible, horrible at t-ball. After I quit, some of my teammates seemed a whole lot nicer. I had thought they hated me, but really, they just hated having me as a teammate.) For most of my childhood, I had little interest in doing anything athletic beyond just being a kid. (Like, I'd play tag, but I wouldn't play softball.) It wasn't until my junior year of high school that I decided to take some initiative to get myself in shape. However, the motivation wasn't fitness itself. My German teacher was the track coach, and his daughter, who ran track, was, well, let's just say she was my primary reason for trying track. She was so far out of my league. She was always really nice to me; we were in the same math class, but she was one of the most popular girls in school, and I was on the math team. Even at the time, I realized how silly it was; it's not like she would have ever dated me. Nevertheless, I don't think I would have run track if it weren't for my infatuation with the coach's daughter. And had I not run track in high school, I probably wouldn't have joined Navy ROTC and served in the Navy after college.
Anyway, although I'm not a child psychologist or even yet a parent, I do think a child's personality greatly affects the strategy required to get that child into physical fitness. If a kid is naturally uncoordinated or shy, he/she may be deathly afraid of joining a team, whether at the age of 8 or 14. And if a kid finally decides at the age of 12 that he/she wants to join a team of some sort, he/she might feel it is too late to catch up to the coordination of other kids who have played sports for years. (That was sort of the case with me.) Since coordination often comes with playing sports, there's a vicious cycle when a kid feels afraid to play sports, whether that fear is social (e.g., being hated for dragging a team down) or physical (e.g., getting hit by the ball). My parents definitely wanted me to be more active, but they didn't force me. They did, however, pay me to run or shoot baskets at certain points, sort of like an allowance. Some people may think that's the wrong way of going about it, but it actually made me more interested in basketball and running than I might have otherwise been.
I think you've got a child who is shy or afraid when it comes to sports, you have to find ways to encourage him/her to exercise on his/her own without fear of ridicule. Yes, it is more fun to play sports with others, but I certainly didn't feel ready to do that through most of my childhood. I do think though it's good for kids to watch sports on TV; at least in my case, it did give me motivation to work out sometimes.
IMHO, it comes down to providing kids role models in whatever you want them to be good at, whether that's sports, academics, or whatever. That, and of course, make it fun. But I don't think a kid is going to find sports fun if he/she isn't going to be able to play without being ridiculed, picked last, etc. There probably has to be a path to fitness and athletic ability that a kid sees before that kid is going to want to participate in team sports.
