thread of ridiculously long posts
this needs to be retitled, “thread of ridiculously long posts” 
We’re not talking about predicting all aspects of life; we’re talking about studying forces on an object in motion at non-relativistic speeds, which Newtonian physics is quite capable of describing. It may not always be easy to describe all the forces accurately, but the problem is only in describing the forces; physics can definitely give you the answer if you feed it the right data.
Momentum=m*v. In a frictionless environment, let’s say one object weighs 10 grams and the other weighs 100 grams. Dropped from the same height, v will be equal on impact, so the momentum of the heavier object will be 10 times the lighter, but it will also take 10 times the force to move, so these two balls, when dropped from the same height, will bounce the same way.
However, that doesn’t tell the whole story, and the reason why not is also the reason why the dropping-balls scenario is not analagous to hopping on a unicycle.
If instead of dropping the balls, you put force into them by throwing them at the ground, given equal force the lighter ball will be moving faster when it hits the ground (F=m*a) and will bounce higher than the heavier ball.
Well the original question was more broad: “Does an extra pound or so on a uni make an “appreciable” or measurable difference in trials riding and/or hopping potential”. I would not be willing to say that it definitely makes an appreciable difference in hopping potential, although I think that’s likely to be the case. I am definitely willing to say that it makes a measurable difference in trials riding, due to lesser energy input required to move the unicycle.
A rider doesn’t magically “make the unicycle weightless”; he puts energy into it on the pre-hop, the tire compression, and the snap upwards, the result being that the unicycle is moving in the direction he wants it to move. The rider can put less force into the 12lb. uni to get it to do the same thing as the 17lb. uni, and I think it’s likely that the rider can figure out how to put the same amount of force into the 12lb. uni as the 17lb. uni and thereby hop higher by some measurable amount.
Take your rolling hop example; if you are limited by your ability to spin the wheel approaching the obstacle, and if your ability to spin the wheel approaching the obstacle is more or less equivalent on a 12lb. vs. 17lb. unicycle (which I think is a reasonable assumption–if anything, the lighter unicycle will spin faster due to less rotating weight), then you’re putting essentially the same force into the unicycle when you hop, whether it’s 12lb. or 17lb. The 12lb. unicycle will hop higher given that identical force.
Hopping is much more a matter of technique than equipment, but that doesn’t mean the difference in equipment is negligible.