bigbulls, you are mixing apples and oranges.

If acceleration is held constant, then time under acceleration will effect the final velocity, however on a bow as gzg38b pointed out, the Potential Energy (area under the draw force curve) is a constant. It wouldn't matter if it took 10 seconds or .01 seconds for the arrow to get off the string, it will only have as much energy leaving as you put into the bow on the draw - the efficency losses (friction, vibration, sound). The only way to increase KE is by increasing the area under the draw force curve (more draw length or weight) or by increasing the efficency of the bow (remove weight from the string, reduce friction etc...) however these changes are all related to the bow and would then cause a change in both the heavier and lighter arrows.