Here is something that I don't think was discussed! It just popped into my head and I am not sure, so bear with me.

As the arrow is leaving the bow, the string is forcing the arrow forward while the air is actually pushing it back!

Now, my thought is this..... where is the majority of the force on the arrow. As soon as it leaves the string, it would seem that most of the energy in the arrow would be towards the back, as there is not a physical force pushing it anymore. Now, as it goes towards the target, wouldn't the FOC mean that the energy would move towards the front of the arrow, which it seems would mean that penetration would increase. Like I said, I am not sure about this, but it is a possability as to why people notice better penetration at further distances!

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.