What McDave says. Bringing the shaft closer to the center of the bow, which is what a skinny shaft does, actually makes the shaft act weaker, or stated another way, enables the bow to handle a heavier spined shaft because it doesn't have to flex as much. To make it act stiffer, you need to build out the side plate a little.
That being said, the difference may not be big enough to notice. The difference between 5/16 and 9/32 is 1/16 inch in diameter, i.e., 1/32 on a "side." I shoot GT 35/55s and Axis 500s out of the same bow without modifying the side plate.