How much should a 13 year old lift in weights?

For a 13-year-old girl: You should probably be able to do at least 5 (real push-ups, not girl push-ups). If you can work your way up to doing 20-25, you're doing awesome.

For a 13-year-old boy: You should probably be able to do at least 8-10 real push-ups. Try to eventually be able to do around 25-30.