I stand to be corrected but as far as im aware a heave line is caused when a horse has to make an extra effort to breathe i.e COPD. I havent heard of one in a fit horse as they shouldnt struggle to breathe if they are fit with no respiratory problems. My old horse had COPD and had a heave line, but if a horse has one there should be more symptoms of COPD that are obvious.
Ditto stinkbomb. I owned a horse years ago that had bad COPD and he developed a noticeable heave line. It's caused by the development of the muscles the horse needs to use to make a forced exhale and it's nothing to do with being fit.