It could probably be easily tied in with the existing toughness, strength, and agility stats.
Carrying lighter objects would encourage the dwarf to run faster, and train agility in the process.
Carrying heavier objects *coughstoneblockscough* would cause the dwarf to be slower (an encumberance system that includes the item being hauled, maybe?). Picking up such a heavy item would be a little strength training in itself, although the heavier the item and the lower the dwarfs strength, the longer it would take to pick up the object in the first place, and would determine overall rate of travel once the speed level is figured in.
Carrying either for a long distance (or maybe just after a set distance in a haul, or by a per-move basis) would help train toughness, which I assume helps the dwarf work longer before needing to knock back a mug of ale or some of that sissy elf-wine stuff, if that's all that is around.
The hauling skill itself would give a bit of a boost to the calculation of stamina/agility (Strength would be if you can figure a way to work it in, a well-versed gripping position that lessens the difficulty of a heavy load, I guess) And, like all other skills, without use, the skill would degrade over time, adding more reason to have task=specific dwarfs
Oh, and the hauling skill would be a great one to also put in pack-animals once that system is integrated and live, since practice makes perfect to beasts of burden, as well.
However, on a side note, two other things would have to be taken into account. One would be the person leading the pack animal/s out to gather things, would also need to train another skill, animal handling, perhaps. The better the skill, the faster the beast can be coaxed to go, up to 100% of it's actual speed based on it's hauling skill and stats. The more beasts a pack-herder tries to manage at once, the harder it is, and needs more skill to overcome the penalties, as well as the increased likelyhood of the beast rearing up and running away, possibly upending it's cart if carts are used instead of saddlebags, and requiring the herder to go chasing off after the beast to get it back to the cart.
Two would be that, unless by some odd turn of warped humor, dwarves actually learn to ride pack-animals, they are going to have to lead them by foot, the speed of both would be the lowest of the two (especially since riding the pack-animal would greatly increase it's load, but a riding system would of course need another skill, and that's too much for me to think about this early in the day.
I hope this makes sense.