It's funny, I've been thinking about this for years. They’re the two characters you’d expect to be the most incompatible - one's a soft-spoken, borderline-psychotic scientist obsessed with unnatural biology, and the other's a giant, sentimental, simple family man who loves his gun and his mother. The dynamic isn't just 'gentle giant and mad doctor.' It's that Heavy's inherent stoicism and his quiet intelligence create this strange, stabilizing anchor for Medic's chaotic energy.
Heavy isn't fooled by the medical degree; he sees the madness plainly and chooses to accept it, maybe even enable it, because it serves the practical purpose of keeping them both alive on the battlefield. In turn, Medic, who likely views most of his teammates as walking test subjects, shows a flicker of genuine, almost possessive respect for Heavy. The Ubercharge is the perfect metaphor: an unbreakable bond of mutual dependency, literally invincible together. You never see Medic that focused or protective with anyone else. Most fics I enjoy play with that professional intimacy curdling into something personal, with Heavy's silent devotion becoming the one thing Medic can't clinically dissect.
And let's be honest, their shared voice lines in the game, that 'Charge me, doctor' 'I am fully charged!' exchange, it’s basically fanfic fuel handed to us on a silver platter.