6'3" and 187lb is nothing, I know shorter heavier people who ride and jump with no trouble at all! My coach would easily be 6'7" and he is an incredibly effective rider.
The rider who I'm trialling a working student position with, I'm not sure how tall he is, but he's a grown man too and looks around average height to tallish (his horses are BIG horses, and he looks just right on them, you'd never guess they are all 16.2+), and he's been to the Olympics.
As long as your horse is built well, and has good strong legs, I don't see any problem with weight. I know horses that can't be ridden by anyone over 75kg (not sure what that is in pounds), and I know horses that don't have any trouble with 300lbs.