Question: I have a ton of the [Unusual Gem](http://www.uesp.net/wiki/Skyrim:Unusual_Gem#Unusual_Gem) items stuck in my inventory.  

It was a long evening, and I have lost the chance to go back to a save point before I picked up the [No Stone Unturned](http://www.uesp.net/wiki/Skyrim:No_Stone_Unturned) quest.

These stupid rocks are taking up 12 "pounds" in my inventory and I have no interest in completing it.

Is there any way for me to drop this quest or lose the super-heavy quest items? A game mod? A dirty-letter campaign to the game designer? Voodoo witchcraft? Anything?

Answer: 
From the quest items page on the [skyrim wiki](http://elderscrolls.wikia.com/wiki/Quest_Items_(Skyrim)):

> 
> While quest items do display a weight, they do not use up the inventory's available space.
> 
> 
> 

So you don't have to worry about quest items sitting in your inventory :)
You are indeed stuck with the gems without the use of console or mod if you cannot complete the quest. 

There may be a mod that makes them weightless (I cannot search the steam workshop myself the coming few days). 

And as @yx suggested, you can use the console if you are on PC with the command `player.removeitem 0009dfbb 24`. 

However, since you seem to have 24 of them I'd suggest trying to turn the [quest](http://www.uesp.net/wiki/Skyrim:No_Stone_Unturned) in. I do not know about the 'not having weight' since they seem to weigh me down.