Well, my wife was 14 and ~80lbs when she did the coursework and graduated at 15. She couldn't even pick up the tank to set it on the bench.
She says you're nuts.
FWIW
Well, not knowing her, it doesn't mean much. I've seen adult divers who were grossly overweight and couldn't even lift their weight belt let alone their tank. They are completely winded just trying to get their wetsuit on. I've seen adults who would drown if they weren't wearing a BCD. They literally couldn't swim good enough to keep themselves afloat. If my son was as inept as many of the adult divers I see, he wouldn't be getting certified. He's grown up around boats, diving, snorkeling, etc.. so he's pretty competent in the water.
Also, We dive mostly from our boat. It's not like he needs to walk a mile to the ocean with the tank. Once you're in the water, you're weightless so who cares? Main issue with the gear is that it fits snug. We have a swim platform on the back of the boat and usually slip into our tanks sitting on the dive platform. We don't even have to stand up with the tanks to get in the water. My wife is certified too and she's pretty petite. She has a hard time standing with her gear on and again it really doesn't matter much. She also has rheumatoid arthritis so she is weaker than a normal person her size yet she still has no problems.
The biggest issue with kids getting certified is how they handle the unexpected and how they can keep their head straight if something goes wrong. The weight of the equipment on land is of little contribution to the danger aspect of diving.
At one of the dive shops last weekend, we suited him up with a BCD and a 50cf tank and he was able to stand and walk around. He couldn't lift the tank with this arms high enough to put it in the BCD but he really doesn't need to either.
I was curious to see what other people's experience was with kids this age getting certified and handling the equipment. I'm think that is the biggest delta between doing it at 10 and 15 but in the end for the type of diving we do, it really doesn't matter.