I have magical weapons with few charges left. I have filled soul gems of various sizes. I want to recharge the weapons. I bring them up in my inventory and press the right stick as instructed to do recharging but all I get is a nice picture of the weapon that I can rotate but no indication of what I should do to recharge it.

What am I missing?

Hit right bumper on 360 when you have the weapon selected in the inventory. This should bring up your list of filled soul gems to recharge.