Several years ago I did some testing with a friend of mine. We were shooting two different bows and two different quivers. Both quivers were 4 arrow. At 12 yds we both had the same results with multiple shots. With the EFA bow quiver there was no difference in the way the bow shot. With a competitor bow quiver we both consistently impacted about 3" left. A week or so later I tried another heavier (different competitor) bow quiver and surprisingly saw no difference.
It left me thinking that the dynamics involved were more complicated than just weight. Factors like how it fastens to the bow, position on the bow including distance to the side of the bow, and front to back, weight of the bow, position of the handle, etc. Other factors might be the weight of the arrow being shot, and shooting style of the archer. Some will grip the handle more tightly than others. Some will shoot with their bow arm straight, and others with that arm slightly bent.
I believe that all of these things can be a factor. At EFA we try to keep the weight end of the quiver (hood) as close to the riser as possible, and the weight and size of the quiver as small as is feasible. As with bow design, bow quiver design will be a topic to discuss for a long time.