Ok, so i just found this out and it has really helped me, so i figured i would share

As everyone knows, having quest items in your inventory when you arent choosing to do that quest can get annoying, and it uses up valuable carry space.
I was messing around and discovered that if you equip the irremovable quest weapon, and then walk up to a weapon rack or weapon display (ive only tried this in my house) and activate it, it will remove that weapon from your inventory i havent tried this on any other quest related items, but i would assume that it would work if you found armor, or books, etc. Again i DO NOT know this for certain, but get out there and try, let me know what you guys find, feedback is appreciated xD

You assume wrong.

Besides, quest items have do not contribute to weight.

Yes they do.

The freaking 20weight Elder Scroll in my inventory for my Warrior characters tells me otherwise

Remove everything else from your inventory. Check your weight. Report back.

Other people are reporting 0 despite the quest items they can't remove.

Edit: And I double checked it myself. 0 weight.

I also tried this while I had the elder scroll. When I remove all of my equipment, it is zero. However with all my equipment I am carrying 102 pounds. When I sold the elder scroll to the orc at the mages college, I was carrying just 82 pounds. Sounds like this may be a glitch of some kind. So quest items do count as weight in your inventory, unless you want to walk around naked.