RE: Who said that physics wasn't fun?
Bigbulls, you have it wrong.
KE is a function of the bow, not the arrow you are correct, but when the string is released, (excluding the losses due to bow efficency) the bow will transfer all of its potential energy to the arrow. The difference between a light and heavy arrow is that for a light arrow it will transfer that energy in a shorter time than for a heavier arrow. Time on the string a zero to do with the amount of KE transferred.
KE is essentially a measure of the area under the draw force curve for a particular bow. When the string is released, that potential energy is converted into kenetic energy. No where in that equation does the weight of the projectile come into play.
Now if we want to look at what happens to the projectile when this fixed quantity energy is transferred to it, we use the equation
KE = ½ mv^2
There is no variable for time in that equation. The amount of time it takes is irrelevant.
Based on a fixed quantity of KE, we can rearrange the equation to come up with:
sqrt((2*KE)/m) = v
With KE being fixed, the only thing in the equation that can effect the final outcome (velocity) is the mass.
As mass goes down, velocity will increase.