It is weightless and can be sold for profit. This item can also be turned into a Leather belt (Dog hide belt) at a workbench if you have a Survival skill of 5 and have the Honest Hearts add-on. This slightly increases its value from 4 to 8 caps. The resulting belts can be used for crafting super stimpaks and weapon binding rituals.
Dog Hide can be found on dead dogs. Although it can be found on most dogs, some dogs won't have it in their inventory.