Has anyone ever weighted the arrow shaft? Is this an option when trying to get a heavier arrow?

Are you talking about carbon arrows,there are many options for adding weight for them.To add overall weight you can try some weight tubes that fit inside the shaft,you can get at 3Rivers.Or you can use heavier brass inserts,but adding weight to the front end will affect your spine in tuning.And you can go with a stiffer spine and use a heavier point to make a heavier arrow.

I weigh every one of mine before I cut them. I weigh them after I cut them. I weigh them again after they are fletched  and have a broadhead on them.