The concept that working out with weights will "stunt" your growth is an absolute myth.
Some of this comes from old observations that many powerlifters were of relatively short stature. The simple fact was likely that they were afforded some mechanical advantage on certain exercises due to their shorter legs or arms, and this helped them reach the upper levels of powerlifting.
That being said, the physis (growth plate) is a structurally weak area in a bone, and is prone to injury, especially in children and young adolescents. Children can start weight training at an early age, but light weights and strict form should be adhered to. Hell, my 7 year-old daughter and 4 year-old son train with me every weekend. They have their own set of 1 and 2 pound dumbells, and I take them through some basic exercises with very strict form. They love it!