» Tue Jun 05, 2012 12:44 pm
Check your "active effects" in your magic menu. You may have contracted a disease that effects stamina or carry weight. Skyrim just loves flinging around diseases.
Aside from that, it could just be a bugged item. Quest objects should be weightless, but on rare occasions glitch up and aren't. After the quest is over, the "quest object" tag is supposed to be removed, activating the weight but allowing you to drop the item; that sometimes glitches, too. Either way, you end up with an undroppable item weighing down your inventory.
This is a bug that started with Oblivion and ran through both Fallouts. You'd think someone would have fixed it by now.