Leverdude has the physics right, but the assumption most people are making is that the heavy and the light arrow are travelling at the same speed. When that is the case, the heavier arrow sinks less due to it's greater momentum- which causes it to be affected less by wind resistance. But if you are shooing a heavy and a light arrow from the same bow- then the lighter arrow sinks less because it starts at a greater initial speed. Try it and you will see. Switch to a lighter arrow, and your pins get closer together. This is because the arrow drops less at standard hunting distances.

Were you to shoot the arrows at a 45 degree angle, the heavier arrow would go farther than the light arrow. But that's not relevant to a hunting situation.

So, yes it's true that a heavier arrow drops less- IF IT STARTS AT THE SAME SPEED AS A LIGHT ARROW.