Your analogy of 100lbs climbing stairs. Are you saying that a truck carrying 100 lbs payload is working harder than a truck pulling a 100 lbs trailer? Wouldn't it be the same analogy? I don't know any of the physics but doesn't make sense to me.
lets look at it like this. I'll use numbers I happen to know off the top of my head.
my 3pt 10' cutter weighs 2400#
at work we have a 3pt cutter in 12' ( why?! ) I can't lift the 12' cutter on my ford 5000 but can lift the 10' cutter with some ballast. the weight difference is just right on that line for my 3pt lift.
I can however drag that 12' cutter semi-mount and cut just fine. In fact, i have pulled my 15' batwing with my 5000 in light grass, but I don't like it as much as having my 7610-s pull either of the mowers.
the larger the tractor, the more weight it can heft around and the more stable it will feel. For instance with my 10' mower raised ont he 3pt on my 5000, if I hit a bump, i feel it, even with front ballast. .. on my 7610s, naa. tractor is quite a bit heavier, less felt bounce.
larger tractors generally have more hp than smaller tractors.
thus, for an implement manufacturer to say that he wants a little more hp for the 3pt version of a mower than the drag version.... he's really saying that he wants a heavier tractor for the 3pt.
since you don't see tractor weights advertised on tractor hoods, but you do often see references to horse power, it's easier to just switcht he weight rec over to saying you need a higher hp tractor when in reality.. you likely need a heavier tractor. ( ALSO.. WITH THE EXTRA WEIGHT, YOU PROBABLY want a lil more hp too, as a makup for the weight trade off. ).