I think I already know the answer to this. When you get your first Unusual Gem before you get it appraised, the weight of it doesnt add to your carry weight right? What about when you get it appraised, aquire more? I know until the quest is complete you cant take them out of your inventory as they're quest items. Thats a decent amount of weight to carry around.

Because its a quest item, they won't weigh anything.

Thats what i figured. Having 24 in your inventory would be a lot of carry weight. Thanks

Don't even do that quest! LoL...
Oh sure, the Crown looks nice sitting there in the T.G. and it is an achievement of course.

But... I just lost 50 weight (struggling to keep my weight below 300).
Know how I did it? By removing 500 flawless gems using the console!
Yes it gets that bad...
When you are carrying 100 weight in gems around, it's bad.

You know what's funny? You can have more than one mysterious gem. Having four mysterious gems will crash your game. So don't take all.

I had a save with 9 unusual gems with no crashing.

I only keep the first one I come across until I get it appraised.

I had 23.