*Puts on Skwisgaar Skwigelf mask* Permits me to dissagree.
If your weapon would gain Skill Points, then that means that if I give my weapon to another player, he would swing that axe with such dexterity and strength. This is not what it is now.
We are gaining Skill Points. Because our skill with the Axe has increased, not the Axe's.
Skill Points are the points that show our affinity to that weapon type. Experience Points are the points that show our character's being, and the more it rises, the more you can place attributes, the more you can customize your character.

If someone tells me "XP is horrible", I intend it as Experience Points anyway. When you gain points there is written how many Skill Points (SPs) and how many Experience Points (XPs) you're gaining, so if you're using the wrong terminology I just go on and say "Yeah, but how much is your SPs?", and if he doesn't know I just explain =)