found on youtube, you opinion?

I don't see a problem with the rationale, assuming it is something the child wants to do and isn't being pushed into it in order to help a parent's wish-fulfillment.  However, I was under the impression that so much weight-training and aerobics could interfere with the physical development of a young child.  Certainly if she is dieting and deliberately lowering her water content in order to prepare for shows or exhibitions, that seems unhealthy for a child so young.