You're assuming a rider leans a bike over using his weight. This is a widely accepted but horribly wrong assumption.
A rider changes lean angle using pressure on the bars. When the desired lean angle is reached, he releases that pressure and the bike maintains that angle.
I think you are correct in suggesting a heavier rider will result in a more stable bike, but ultimate stability is not what racing is about. A heavier rider will tend to contribute to a greater roll moment, possibly canceled by a heavier rider's superior upper body strength.
In steady state cornering, I think being a bit heavier may be an advantage because you can more easily relocate the center of gravity to the inside, thereby increasing the effective lean angle. However, this may be counteracted by being harder on tires. And, obviously, straight line performance will be negatively affected.