You know when you steal a weapon from someone/someplace, and you drop it, it has its name in red color (says "Steal" rather than "Take"), and you can't pick it up again while being detected by an NPC, else they catch you stealing it again and take it away from you as well as all your stolen stuff.

So the way to get the stolen status removed is-

...some NPC/enemy must pick it up from the floor, then you kill them, and the stolen status of the weapon is removed so you can take it from their corpse. They only pick up weapons if they are on alert state, not if they are in calm state. And you can't reverse pick-pocket the weapon in their inventory and kill them, else weapon still has stolen status.

And NPC only pick up weapons if it is better than the one they have. Even if they don't have ammo for it, they will still pick it up.

Obviously since they don't pick up outfits, this tip is only for getting stolen status of weapons removed, and not apparel.

Some say that fencing to merchants work, but it has never worked for me (I play Xbox version).

What are you stealing that you need to do this? I've never had this issue, ever?

Decorating house.

If I was on PC I would use the console command SetOwnership. Just a tip

The wiki says Cliff Briscoe is a good fenc- I mean, pawn shop. Sell to him, exit the shop, and buy back. Voila!

Well, that's what they say. I never steal, I kill and loot

Ranger Sequoia from Chief Hanlon?