Okay, I didn't really want to join in on this discussion, but since this is one of my main classes, I better say something too.
First off, I'm against class limits in general, though I think teams with 5x of anything are doomed to fail, so there bound to be some restrictions. Secondly, I'm against the class limit of 2 for heavies, but I'm not against testing it for a while just to see the effects.
Now to why: in my opinion, the "might" of the heavy is misrepresented here by a scewed perspective on our server. Let's be clear: most heavies on our server are exceptionally good. Whatever you may bring to the table with maths, HP values, damage values, speed and so on - if you can't work it, you won't kill shit. It's the same basic principle that works for every class. Your class only becomes powerful, once you know how to utilize it's strengths and minimize the effects of its weaknesses.
True, in current form, there are several loadouts, that make playing heavy easier and which also remove some of the weaknesses of the heavy in some situations, but same goes for every class. I'm not going into detail here on purpose, because in the end we could do this discussion for pretty much every class. Yes, heavies are a pain in the ass to kill, but they are just a sitting duck with plenty of HP and if you get killed, well guess what, the general rule in this game is "Don't get shot".
I agree the annoyance (as with every other class) gets magnified by one or multiple medics on the heavy, but again, this is also valid for every other class (within reason, no one is going to pocket an engi, I suppose). The valid responses here are also heavies, medics, ubers and teamplay. They aren't invincible (at least not longer than 30 seconds, right, John?

) so just kill 'em.
Seriously, I would be all for this suggestion, if:
- we had much smaller teams
- heavy had no counter (kritz, sniper, spy, sentries, DEMOMEN, other heavies)
But neither is the case. Since I play demoman, I learned how easy it actually is to kill a heavy. You need to hit him three times to make him run, medic or no medic, if you are using stickies it's even easier (though I can't use stickies).
That said, I'm not against a trial period, but I will make sure then, that there are always two heavies on my team.

Not a warning, just a promise.