I think recharging enchanted weapons requires a certain perk.
Yeah, I just looked it up, you have to be at least level 20 in Enchantment, and then get the perk Soul Squeezer. Then go to the menu, where you can pick between, skills, items, map, magic... go to items, then go to weapons. Then go to weapon you want charged. Look at bottom of screen, and ti should give you the option on how to do it. On the PS#, it is R2, then select the soul gem you wish to use. It must be a filled soul gem.
Hope this helps