If you have more than one bound weapon spell (axe , bow , dagger , mace or sword) , go to the arcane university , and create a custom spell with more than one bound weapon effect , the spell can be very short (5 secs.). When you will cast the spell , the spell will attempt to equip the weapons in alphabetical order , the game will equip the first weapon and the others will remain un-equipped in your inventory. Before the spell expires go into your inventory and drop the un-equipped bound weapons , then wait until the spell wears out and pick up the dropped weapons and voila permanent weightless weapons.

There are many advantages for doing so , for starters unlike umbra that is also weightless (until the relative quest is activated) bound weapons will NOT tire you when you swing them they are truly weightless. Also , being weightless you can reverse-pickpocket them to your followers , and since they are of daedric strenght your followers will equip them. Also the bound sword (which is a claymore) has a base damage of 31!!! the highest i have seen in the game (after mastering blade , of course). Also after enchanting bound weapons , they will remain weightless , so having 10 of the same bound weapon will allow you to never needing to recharge them , when they are depleated simply discard them.