In addition to increasing their attack power or giving them unique effects, combining your weapons with different materials can also increase their durability. Not all materials are valid, although there are some about which there is no doubt, such as stones and rocks; and materials that come from monsters, such as horns and fangs.
Bonus Tip: To return a combo weapon to its original state, open the saddlebag, select the weapon in question, then choose the Undo Combination option. Of course, remember that you will lose the material that you combined with the weapon!