It would but it wouldn't be worth it in a featherweight.

A counterweight wouldn't be able to be positioned far enough away for it to be of use.

Lets say you have a 1kg head on the axe. If that's at 50cm distance then you would need a 2kg mass 25cm on the other side, or a 5kg counter balance at 10cm distance. Much better to look at the placement of components in the robot itself or use magnets if fighting in the robochallenge featherweight arena.