What sort of heavy breathing is it? Is it like this video?
Cantering Horse High Blowing - YouTube
If it is, I've known many horses breath like this (I've always known it as high breathing), and found it tends to be in horses that are more excitable. I used to school a big thoroughbred gelding that used to high breathe in canter, every stride was a big snort, and he was a pretty successful eventer in his day.
If it isn't that, it might be worth getting him scoped after all. What breed is he? I'm only asking as I know roaring is more common in Thoroughbreds, and it generally makes itself known at gallop.