Exercise stimulates growth plates, by putting pressure on bone cells, forcing them to specialize and create new cells. Too much pressure, however, damages the growth plates, which are soft and fragile...The rule of thumb is that lifting one's own body weight (in push-ups,pull-ups, etc) is fine at any age, and kids over fifteen can lift weights.
Arianne Cohen, The Tall Book: A Celebration of Life from on High
growth, height, weight-lifting