Fascinating, useful, inspiring: a good read. But if I may take the discussion back to the thread about redefining physics:
As has been pointed out, the relationship between distance hiked and weight is nonlinear, but how close to linear is it if you count system weight rather than just pack weight? It's exciting to talk about getting your pack from 30 lbs down to 10 lbs, but this conveniently ignores the heaviest part of the system: you have NOT reduced your weight by 67%--you've actually just gotten your weight from, e.g., 200 lbs down to 180 lbs--a reduction of 10%. Subjectively it seems that this creates an improvement greater than the 10% suggested by the math (due to the vagaries of biped propulsion, I guess?), but it's not going to reduce your energy expenditure by anything like 66%. What is the real observable improvement? BPL seems the most likely candidate to do a useful study of this subject.
I'd hazard a guess that some desideratum (e.g. distance hiked) is probably nearly linear (or probably affine, but that'd be interesting to know) over a "relevant" range (say, pack weights from 0 to 50 lbs). But it'd be nice to see what that linear-ish range actually is. It would make the whole cost vs. benefit analysis of carrying a tent vs. a tarp, or investing $x in lighter gear, far more compelling!
The human is a source of some difficulty: we change over time, we're probably optimised for whatever weight we normally carry, and if we lose 5 lbs, the way in which we lost it affects our output. So one study might concern keeping people as constant as possible (or averaging over large numbers and controlling for changes in fitness and weight) and measuring distance hiked with varying weights over some "laboratory standard" terrain, and another might be "What's the best way to lower your body weight for backpacking?" Here I suggest focusing on the first one, just because it seems to directly address Will's, um, artistic license.
The data will be extremely noisy, so this would not be a small undertaking. But I think it'd be extremely enlightening (ha).