Why do we attempt to reduce the weight of our packs? Another way of saying that is, what is the price of additional weight? It is a rhetorical question, but a short list might be:
1. More work to go the same distance (work in joules, ergs, foot pounds, etc.)
2. More displeasure (less fun) with more weight
3. Pain (sore back, muscles, chafing.
4. Less distance possible.
5. Less speed possible.
6. Elevation gain more difficult
Now suppose you sum up all those things as some quanity. Call it effort. That quanity is a function of weight. That is to say more weight equals more effort. But it isn't a simple linear relationship. It seems to me that carrying a 50 pound pack is more than twice as difficult as carrying a 25 pound pack and at some point it becomes quite impossible. So I strongly suspect the “effort” is increases quickly with the back weight.
So we have a quanity we want to model with respect to weight. Effort with respect to weight. Perhaps it could be expressed like this: Effort is a function of the weight to some exponent. If y = effort and x is weight then perhaps y=x^n and we can throw in a constant. y =ax^n. Or written a slightly different way f(x) =ax^n.
If n =2 then if you compare say 20 pounds with 40 pounds it isn't twice the effort but rather four times the effort.
Does quantifying the relationship like that make sense to anyone?