I would assume there would be a point forward where weight wouldn't matter, but I think arrow diameter would. To some degree, arrow diameter changes center shot. In practice however, that point may be far enough forward to not matter.
If the arrow is already on the verge of to light, I would think anything center would have a dramatic effect, and a less effect as you neared the ends with some sliding scale where the back has more effect than the front. The back gets the brunt of the force, where the weight of the arrow causes the front to feel less trauma, so it could theoretically be lighter.
But I'm still on my first cup of coffee, so there may be a caffeine deficiency flaw in there.