Now, as far as arrow weight goes. I have always used the analogy of which would you rather be hit with, a bowling ball going 10 mph, or a ping-pong ball going 100 mph! Sure, it is "far fetched", but it is one way of thinking. A heavier arrow is going to carry more momentum, and that momentum is what gets the arrow through the deer. Like others have said, a heavier object is going to be harder to stop than a lighter object.
That ping pong ball would have to be going A LOT faster than 100mph for those two to be anywhere near comparible. THat ping pong ball is a lot less that 1/10 the mass of the bowling ball. Good idea though, I can see your point.