Jake,
By way of comparison, I am also 6 foot 3 but only 200 pounds. In terms of fitness, my double steel 120s weigh just shy of 100 pounds when full and I can comfortably get into the water and climb the ladder with them afterwards. Truth is BMI means very little. You should consider your body fat percentage (I am at about 22% which is a touch high for a male looking to do serious diving). If you are happy to do OW, AOW and rescue you will probably be fine. It sounds like you have some doubts, so why not check with the doctor?
Cardio is important. At the age of 15, your body is probably young enough to handle what you throw at it. It is a game of statistics and chances of a heart attack are higher once you have tripled your age, but for you that is still two lifetimes away.
Even so, under stress conditions persons with poor cardio are more likely to gulp air and over breath a regulator. This is especially true if you are in a current or other difficult conditions. Basically this gives you a greater risk of panic and doing something stupid when your are in tough conditions. I actually know of one case where the cause of death was panic and bolting for the surface after someone couldn't fight a current with the rest of the dive team and started to lag behind.
Different body tissues off gas at different rates. I am not an expert, but from what I have read, fat tends to have poor circulation and off gas a little slower, so set your computer to be conservative (or dive the tables conservatively). Again probably not a major issue if you are within recreational limits.
Overall, I would say check with a doctor, do the course, dive within your limits and have fun!