Do quest items weigh anything?

Someone said that quest items don't count against your carrying capacity in Skyrim, even if they have a weight listed. Is this false?

No

Quest items weigh nothing, even when there is a weight listed.

I personally had this happen with a stack of Alto wine, I had over 140 Alto wine, while my total carry weight was below 70 (Alto wine was weighs 0.5)

Correct answer: It depends

I have some quest items that DO NOT add to my weight. (Someone's axe that I need to deliver)

I have other quest items that DO add to my weight. (Someone's sword that I need to deliver)

It seems that quest items that DO add weight, can also be removed from your inventory and dropped or sold. So I guess they are not "technically" quest items, though they are needed for a quest.

However, there are also items that DO add weight, but can not be removed from your inventory. Such as a quest item for a quest you do not have yet.

No, quest items do not take up weight.

For proof, drop everything you can drop from your inventory into a container; your carried weight will be zero.

If you would like to get rid of your quest items from your inventory, drop all your dropables in your house and keep 1 lock pick, than pickpocket a guard. Get caught, go to jail and escape without recovering your gear.

All the non-droppables will be safely kept in the jail's evidence locker.