So, the Heavy is out in left field when it comes to the other combat classes. He is both slow and short ranged, which are huge disadvantages. How does the heavy make up for this apparent lack of combat ability? Lots and lots of health.
Props to Open Office
I am going to posit a hypothesis that giving a class in an fps double health is a terrible idea. Many people out there are going to disagree with me on this and say stuff like "I don't want to play a game with a lot of identical characters." To which I would reply "Having double the health of the average class is not interesting or fun, so lets come up with something better."
Spies, while suffering from the same problem of slow speed and short range have a cool advantage in cloaking. Pyros, another short range and slow class, get the airblast. Engineers can throw down sentries. All cool abilities that add to the depth of a game. Having a lot of health does not add anything to TF2 besides a roadblock.
Having lots of health is the most boring advantage ever. It doesn't take any skill to move around slowly while eating rockets to the face. The majority of the heavy skill set is to find a good place to stand and shoot at people until he dies because the heavy isn't going to be able to retreat or once he spins up.
This is boring for the heavy, because he has no interesting decisions to make, and boring for anyone shooting at the heavy, because it isn't hard at all to shoot a heavy. For most good players the biggest deterrent for engaging a heavy is that it takes so much ammo to kill one the enemy team can come in and kill you while you reload. I used to play on a 6v6 team that would run double heavy on the last point of gravelpit style maps because it was literally impossible for your average team to kill two heavies without wasting time by having someone switch to sniper or spy. While it was funny seeing the other team rage it wasn't actually fun to execute.
I will go more into health and how it affects balancing in part 3.