You can't upgrade items at the moment, but you can get items that are more and more powerful. As you advance in the game you will be able to find new objects, you can also create them yourself from the shelter workshops.

You will be able to make different weapons, ranging from melee weapons, ranged weapons and others of chemical origin.

In the three options you can make weapons of two types of qualities:
Uncommon and rare rarity weapons, it all depends on the type of blueprints you have.