There is no scientific evidence to support the widely-held erroneous belief that increasing exercise reduces child obesity. On the contrary. - See this article from the Guardian: Glasgow University Study finds that increasing exercise does not reduce child obesity.
When children become fat it is essentially because they are eating salty food. Children are especially vulnerable to salt because of their small size and small blood volume, and because their blood vessels are weaker than those of adults. Salt, and the water it attracts to it, can more easily distend weak blood vessels than fully mature ones. The resulting increase in blood volume and other fluid retention results in weight gain, as well as higher blood pressure and many other undesirable consequences. The smaller the child, the less salt they should have - and a baby, of course, should have no salt at all. - Babies can die if they are fed salty food.
Because children have much smaller bodies than adults it would be best if they had no more than half as much salt as adults. Most children, however, have much more than this because they eat so many snacks and instant foods. Just one cheeseburger, for instance, contains almost double the recommended daily salt maximum for children. There are high amounts of salt in packet soups, instant noodles, ketchup and sauces, sausages, burgers and savoury snacks. Fat children will lose weight fast if they eat less salt. And even faster still if they eat plenty of fresh fruit and unsalted vegetables, because these are rich in potassium, which helps to displace sodium from the body. Overweight children should not be put on a diet; dieting is harmful and unnecessary and does not usually result in weight loss. Once children start dieting it is often the beginning of a lifetime of yo-yo dieting and increasing weight and ill-health.
and Sodium in foods