I am not sure that gravity will slow the heavy arrow faster...it (gravity) is only trying to get the arrow to move in the vertical plane (arrow drop). But a heavy fat arrow will have a very similar effective specific gravity as the light skinny arrows. Even at the extremes, you won't find the light arrows to fall to the ground any faster than the heaviest arrows.
The force we need to deal with is wind resistance (cg). For all intents and purposes, arrows have a similar cg. Hence the arrow with more momentum will fight the wind better. Wind it the only force trying to slow the arrows, not gravity. Gavity only wants the arrow closer to earth. Being that the cg of most all arrows is similar, the one with the most momentum will keep it's speed longer.