For sake of the discussion----lets assume you are taking a half dozen arrows into the woods. No matter what quiver you use, the arrows still weigh the same. The variable would be the quiver itself. If the object is to reduce the weight on a hike, what kind of quiver would be lighter than a side mounted bowquiver for example?
I like the bowquiver because it is convenient to me, easier to navigate through thickets, and if you have your bow in hand, you have your arrows too. As for weight, whether shooting or hiking, it adds almost nothing IMHO.
However, my way is not the only way or best way for everyone. But for a strictly utilitarian kind of quiver---I like the side mounted bow quiver.