Yes, open up your inventory and look at the weapons. Underneath them is a Bar, the amount on the bar you see is the charge. I used to think it was the level if diss-repair, but on weapons it's the enchantment.

Note, just in case you don't know this, right click on the weapon and choose Charge to refill the Enchantment with a Filled Soul Gem. There is also a key stroke to do this, but the tool tips tell you that, I don't remember it. You can use lower level Soul Gems to fill it up, it will just take a few of those, on level gems just take 1.

Another cool trick is you can effectively recharge the enchantment by applying a new Glyph. So, if you have a base game enchanted weapon or used a white glyph in the first place, then you can replace the charge from mob looted Glyphs, without burning a soul gem.