Which division is greater? Middleweight or Heavyweight?

Yes, but the bottom line is. The heavyweights can beat the welterweights in the sport of boxing. Ergo, they are better at boxing.

 

I agree, but on average the HWs win, as you point out. That's the important point.

Weight classes started when some good old-time boxers who might weigh 9 or 10 stones, having tried or been considered for the championship of boxing, decide they're probably not able to be THE number 1 champion or don't fancy taking on another huge man, but challenge anyone "up to X amount of weight" .
Someone the right size accepts the challenge.
The fans want to see the fight, etc.

 

The thing is that superiority comes from the group not the individual. A LHW Steve might beat HW Bob but Steve isn't viable at HW and Bob is.

Boxing especially now is built on winning almost every single fight. If a fighter fights 30 guys they are better then who are the same size their chances of going 30-0 is much greater than if those 30 guys were HWs. Even if the little guy should be favored in every single fight the chance of any given one pulling the upset is much higher and the fighters chances of going 30-0 is much less.