I've got quite a few, but I'll compile some of them into a little list. I headcanon that:
-Cheavy's first name is Mitch, and his last name has gone through several changes in attempts to hide his identity. He doesn't really remember what his real one is, only his most recent one.
-He started working as a mercenary closer to the time Medic was born, ~1915, in his late 20s. I could very easily see him as the oldest Classic mercenary in his late 70s - early 80s. He would have been on the Classic BLU team later in life, however, closer to his 40s.
-Cheavy was born somewhere in the Midwest, but not the same state Soldier was born. I'm thinking Michigan (or Utah because the only good thing from there is the Utahraptor named after it lol)
-Had past flings with both Classic Medic and Classic Pyro, with Bea being a rebound after it didn't work out with Cmedic (aka he left to work as a Nazi doctor and then got deboned by tf2 medic). Cheavy got cold feet with the idea of him and Bea having something more serious like he did with Cmedic. His future relationship with TF2 Medic would similarly be a rebound of the first one, wholly unaware that he's exactly the reason his first love never returned.
-Cheavy is a strict domtop and hates being seen as weak or being overpowered, seeing his position in a relationship as a form of power. However, one of his most shameful fantasies is exactly that - being overpowered or otherwise incapacitated (drugs, restraints, violence) and forced to play a submissive role. CNC and noncon potential is abound, especially with someone like TF2 Medic.
-He does not particularly care for animals, especially not Medic's doves, but he does have a soft spot for big fluffy dogs that can double as powerful allies, such as Caucasian shepherds. He had a puppy as a kid that doubled as his best friend.
-Cheavy does not care much for labels, especially not for sexuality. To him it's not gay if he's wearing the pants, even if the relationship becomes a serious romantic one, but for all intents and purposes he's bisexual with heavily internalized homophobia several degrees stronger than Scout's.
-His dick is the biggest Medic's ever taken, and that's saying a lot. Bigger and thicker than Heavy's, with the libido of a demon that even Medic has trouble keeping up with, thick as a coke can and an outright footlong. Thick foreskin and very veiny too, and even if he's losing some hair on his scalp he's got quite the thick, greying bush. Heh, and Medic thought he'd make light work of Cheavy due to him being a grandpa (metaphorically; he does not have any children let alone grandchildren that he knows of. aside from that baby baboon)

And knowing the Medics, it's not gonna be all talk. Especially with the bonesaws for the tougher parts, though he might like teasing Heinrich by making light cuts along the lines with his scalpel first. Or maybe keep it to that, lap up the blood, let him succumb to bloodloss or keep him on the brink. Lifting his balls by the side of the bonesaw and telling Heinrich his sweetbreads will make a nice bite-sized snack and laughing at the whimper that gets out of him. Warning him that he oughta not squirm too much, lest he lose them before he cuts the rest of him up. Saying he wants to save them for last. But a little taste couldn't hurt, sucking him off while slowly cutting along the dotted lines on his thighs. Of course making sure to keep Heinrich on the edge, gotta make him last the whole process. Thus it'll also have to be quite slow, keeping him in the infirmary for hours.

The labeling itself won't take too long, though Ludwig still teases him throughout it. Telling him how good he'll smell once he gets him in the oven after all is said and done, maybe if he's good he'll save some of his own meat for him to taste once he comes back. How pretty he'll look with an apple in his open mouth, and that he'll be keeping the head as a decoration. Calling him piggy and saying he's fattened up nicely, poking his belly that's really not much plumper than Ludwig's, that his meat will be nice and marbled. Calling him a nice piece of fuckmeat as well, that he'll stuff him once the butchering process is done and record it for memory's sake (implying he'll also let BLU watch RED fuck his corpse once he respawns), would be a waste not to use every part of him.

Perhaps BLU suspects it somewhere in the middle of it that there's gotta be more than just surgeon's precision making things seem so easy for RED, that this likely isn't his first time. And Ludwig confirms that, telling him he's butchered plenty of other people in the past, men that unlike him, wouldn't be able to come back and see his handiwork to completion like he can. Also saying that he's one of the few more willing ones, and he has a feeling he'll taste much better as a result. Less cortisol that way. Heinrich's considering himself in equal parts incredibly lucky and unlucky, fulfilling a fantasy with someone so experienced and not having to even truly die to see it through. But that Ludwig would have no qualms with carving him up and eating him even if that wasn't the case. Ludwig only lets Heinrich cum when he's about to die, and the last thing he remembers before passing out is the vague sensation of a blade cutting his sweetbreads free.

With the medigun on just enough to keep the vivisected Medic alive, but otherwise being in excruciating agony. Other Medic watches him writhe in pain and that's enough to get him hard. Perhaps he'd like to feel the power of killing a god, but then, who would he worship? Even if he'd come back, what kind of devoted follower kills their god? So instead he decides to pay tribute, aiming right for the organs, grotesque beauty on display. Shimmering and throbbing and covered in blood and other fluids, Medic finds himself wishing he could dive in and eat them. Like some twisted take on the blood and body of Christ communion. When he cums on them, Medic makes the ugliest, goofiest cumface his counterpart has ever seen and whining a prayer pathetically, thanking him for allowing him such divine pleasure.

Maybe the worshipped Medic hates to admit to finding some enjoyment, or at least arousal, in the whole experience. Hence being hard, and his tormenter/follower deciding to return the favor. It's made all the more agonizing with the pain having yet to let up, innards still exposed and being eyed hungrily. He bleats out a little "yes" just so he can cum, not really caring where it happens in the moment. Worshipper Medic makes quite a show of savoring the cum in his mouth and taking his sweet time swallowing every bit, licking the remaining traces off his lips and fingers, immediately saying he wants more. Cue going straight from intense edging to overstimulation that would make the edging session bliss by comparison, intending to drain his god dry.

Ooh boy, those two being allowed near one another that early on is a recipe for disaster. Mickey bring Ludi small and dead animals to run experiments on (for the former) and dissect (for the latter). Or knowing those two they probably put a dead rat up either of their asses or something. Not to mention the urine/stool sample angle, Ludi already being somewhat familiar with what types of procedures are performed at clinics and knowing exactly what he wants to do when Mickey hands him a jar of piss (or lobs a water balloon filled with piss at him). Point being they'd both be worse off with more time and opportunities to indulge each other's nasty habits and desires had they been allowed to meet back then.

Could see it either being the result of the other Medic breaking him during a particularly brutal interrogation, or yandere Medic. In the former scenario, the other Medic enjoys the attention and laughs about how pathetic he's acting, enjoying that he can say and do anything to him and he'll just take it on the chin. He'll even throw battles for his counterpart's sake. Maybe eventually the mindbroken Medic gets kicked off his team for how incompetent he's become thanks to his obsession, in turn gets taken in by the other Medic and kept around as a pet. In the latter scenario, enemy Medic is instead creeped out by it. Initially he agrees, he's great, he's a god, he's certainly better than him. But then the following around gets on his nerves, and it gets even worse whenever he tries to push him away. And then one day he decides to make him into a macabre art piece, kidnapping and restraining him in his infirmary and vivisecting him. Saying he's always wanted to see what was inside a god.

Yeah I could see it. Maybe he likes turning others (or himself) into terrifying bloodthirsty (or incredibly horny) monsters to fulfil his power/being overpowered fantasies. I think he'd like the rush of feeling so much stronger as he slowly slips into his new form. Or savors the pain and sorrow of the other person as the painful transformation turns them into a hideous conglomerate of sheer agony, like a sentient blob of flesh and viscera.

To be honest I have a bit of a niche kink for droidification which combines latex, transformation and hypnosis. In which perhaps Medic (or someone else subjected by Medic) feels sentient black goo encase them and slowly transform their body into something more useful to be a good little pet droid. Maybe robotification instead where Medic gets captured by Gray Mann and the robots hold him down as liquid metal encases and turns him into a good lil medicbot, including his legs becoming the wheel, his eyes becoming optics, his dick either being forever locked away, disappearing entirely or becoming shaped like a drillbit. And throughout it all he's simultaneously horrified and aroused.