Wow, this thread is sort of all over the place. I have some pretty strong opinions based on our experience and what I consider to be fairly deep knowledge of strength and performance training for athletes.
1) There is no reason for a 13 year old NOT to lift weights. Our societal dissaffection for resistance training ("I want to be toned, not bulky") is non-sensical. The physical and mental benefits of resistance training are manifold and it's not just about packing on muscle. First, the kid develops a gym habit. Think that's stupid? This stuff barely gets taught in school anymore. Kids that train as kids will continue to seek out fitness advancement through life. Second, neurological training and motor patterning. Much of the unseen beenfits of lifting are refined signalling and muscular recruitment during extertion. That stuff is not automatic with aging. It has to be developed. Third, soft tissue thickens in repsonse to time under load, regardless of hormone load in the body. This means stronger attachments between muscle and bone, thicker ligaments and tendons, and better structural capacity to defeat our friend Mr Gavity.
The issue has been researched and the research has been published. The only proviso in a few studies I read was to ensure adolescent lifting be conducted under the supervision of an experienced trainer (but not the guy selling memberships at your local big box gym 
). See "programming" in #3 below.
2) As to strength deficits with "symptoms" like "knees move inward on landing," the commenter above is totally correct that this is very common. My lifting coaches constantly cue even their adult lifters on "knees out" on the eccentric movement for squats, cleans, deadlifts et al. One way to cue the knees out is to use a thera-band at the knees during squatting or other similar exercises which forces one to mind and create mild outward force during the lift (both going up and going down). My son started this practice at 13 for front squats in particular, and continued until he was well into the mid 200's on his front squats at 16. He'll still do it occasionally now that he's back squatting just to reinforce the motor patterning. But his form is really clean.
3) You might get better value (if you are willing to pay for it) to break down and pay for training in a more boutique Strength and Performance setting. Depending on the facility and it's conditioning model, your child's performance and overall athleticism will improve on a sound foundation. Better facilities are run by folks that are actually trained in things like multi-modality programming, safety, and will have the right equipment for the job. The doufous at 24-Hour Fitness will have him doing 3 sets of 10 on machines that have no use outside of the PT setting.
I really recommend #3. My son started physical training with me as a 12 year old. I learned to lift old school style, at school, on my own, then consumed everything I could to learn about physical fitness. I never quit that. At 13 our baseball club had a full gym facility with two trainers. They got him started on gym habit, but in the end knew virtually nothing about programming and mixing modalities. By 14, I had him in a facility run by a former Clemson /Tampa Rays player who liked to say he majored in "lifting weights." Being a baseball guy he is fully tuned up. But he also happens to have a degree in Kinesiology, is a continuous learner and applier, and oh, he's a physical therapist. Tada!
