You are wrong the best predictor of speed over an assortment of different weight arrows is virtual mass, which is based on stored energy and efficiency. The lower the virtual mass the less drop in ke as arrows get lighter.
I assure you that the laws of physics say what I wrote is 100% correct. The only question is how much the efficiency (as defined by what percentage of the stored energy is transferred into the arrow) changes between the two arrows.
Is there somewhere that explains how you calculate virtual mass?
I would also enjoy seeing OP test a few different arrow weights (if possible). It would make for an interesting experiment.
Mark