A weaker spined arrow will move a bare shaft impact to the right. It has the opposite effect on a fletched arrow. In other words, a stiffer spined arrow will move the impact of a fletched arrow to the right. A weaker spined arrow will go through more paradox than a stiffer spined arrow, and leave the bow with the nock end left of the point. This orientation isn't corrected with a bare shaft as the shaft moves downrange, and causes the bare shaft to impact to the right. With a fletched arrow, the fletches quickly correct the nock left condition, but the arrow itself has been moved to the left and stays to the left downrange. Changing to a stiffer shaft will reduce the leftward movement as the arrow leaves the bow, and cause the fletched arrow to impact to the right of an arrow with a weaker shaft.
The effect I described doesn't occur 100% of the time, depending on the differences in spine and how close or far out of tune the arrow was to begin with. However, it occurs often enough to be a good general rule.