Well, I assume water skins are heavier than bags exactly because they're water proof, unlike the bags that shouldn't be (or else the contents would risk getting moldy fast).
Also, since bags have a higher capacity, they weigh a lot more than a water skin when full... You typically don't need to haul more fluid than a waterskin's worth between topping up anyway (and my characters usually don't carry any water at all, but that's at least partially because the Nerp Cooking Mod's goulash and, in particular, borstch, contain some water).
Hm, I do carry a wide range of containers, for different purposes, and different names and sizes help me to organise it a bit. Skin is too small to me - I need more (or less - birch-bark box), because I often make use of hideworking skill in the place where the animal was killed. Often it has no water. The same with cooking. My dog carries some pots (to make soups, mushrooms and herbal beverages, which I use a lot), while my bull carries some tubs of water, but I have to carry some water (bowl preferably) on my character's person, because animals often are dumped or tied some tiles away for safety, and I want the cooking going before I start looking for them.
Also a character has to drink very frequently, so both while wandering and while spending time at home I just have to have water, even without making hides. I live in caves only, and they rarely have water nearby.
However, the main reason skin is bad is that it has lesser volume than a cooking pot. So bowl (identical volume) or something bigger is needed to empty the heavy pot quickly.
The biggest inconsistency is that skins require 4 lbs of leather to make - while they weight 0.3 lbs. I wonder what happens to the rest. When you make a shirt, it takes as much material as it weighs later.