You may need to alter the duration of the Soul Trap, or lower the amount of Uses on the Weapon. If You are using Mods, Read The Readme of any Mods that affect Enchanting.
I don't have it on the weapon. That's my problem: I can't get it on the weapon. When I try to enchant the weapon, I get that message. What is the "charge" they're speaking of?
I highly recommend bookmarking this http://www.uesp.net/wiki/Skyrim:Enchanting and using it as an initial resource for all your Skyrim confuzzles. That said, when you enchant a weapon, the first time you select an enchantment like Fire Damage you get a menu to pop up with a slide bar. This slide bar allows you to change the number of charges a weapon has (that is how many times it can be used before it runs out). Slide the bar back and forth and read what it changes and adjust it until it allows you to enchant. If that doesn't work then I would recommend purchasing a filled soul gem from a vendor and see if that works. This may indicate something buggy with the soul gem that was filled via soul trap. Hope that helps. Cheers!