There's a long debate going on to whether they encumber you or not, but for me it's not about weight. it's about clutter, I am literally fed up of worrying that the next item i pick up could be stuck in my inventory for the end of time, it's ridiculous, I've gone so far now as to only do quests that i know i can complete with a clean Inventory. So that kind of ruins the game for me..not trying new things, sticking to one routine.
Whats the solution i hear you say? Safes...safes should be used as a quest item container so you can actually store all your quest items in them..it really is that simple.
Or even better, let us drop them regardless of how far we are in a quest, just because Mr. dumbo dropped a vital quest item and now cant find it, doesn't mean it should never leave your inventory.
just my two Septims.