I believe that most of what has already been said is true. Putting a bow quiver on a bow properly shouldn't require stiffer arrows, but sometimes it does. It has to be due to torque.
There is more to it however than just the weight of the quiver and arrows in it. How it fastens to the bow, fastening mechanism, how it is positioned to the side of the riser, and how far from the riser can all be factors. A bow quiver acts as a stabilizer to the bow, but it can have an adverse affect depending on the weight and positioning.
Several years ago I conducted an inhouse test using our EFA bow quivers and several others on the market. Someone else, shooting his bow, was shooting the same sequence of quivers that I was with my bow. At about 12 yards (inside) we shot first with bare bows to make sure we were "on". Then we tried two different EFA bow qivers. The results were the same as with bare bow, with no noticeable change. Then we tried two other quivers from other manufacturers. Both were heavier then the EFA quiver. One of them showed an obvious shift of the arrow impact of about 2" to the left. (Same results by both shooters on the two different bows.) When we went to the third quiver, which was heavier than the second one, much to our surprise, it shot similar to the bare bow.
What this says is that there is more then weight involved here. You can add weight without necessarily changing the center of balance of the bow significently. If you feel a change in the center of balance of the bow then you will probably see it in how the bow shoots.