The weight makes a BIG difference depending on the arrow's spline and the bows draw weight.
If it's too heavy, you will get too much flex in the arrow at release. If it's too light for the arrow you will not get enough flex in the shaft at release. It also makes a difference in how the arrow is balanced, I'm at work and don't have my book, but it makes a difference where the center of balance lies on the arrow's shaft. (Just forward of center, I think) Makes allot of difference to the "highly tuned" rig.
A word of WARNING if you are shooting carbon arrows check with a knowledgeable archery shop if in doubt when choosing a tip for light carbon arrows. A tip that's too heavy for a light arrow can cause the arrow to explode when you release it. Expensive and dangerous. I saw what it can do. Painful!!!