In Fate Core are there any mechanics to level up the items you are holding or do they have set mechanics?
Supposing you're talking about important items that are integral part of your characters and story, they should be handled as Extras. In Fate Core Extras advance at milestones, much like characters do.
Quoting from the Fate Core manual (page 276):
Extras and AdvancementExtras advance a lot like their base elements do, according to the milestones in The Long Game. That gives us a set of base guidelines:
Of course many extras use more than one element. We recommend that you allow the players in your game to develop the separate pieces of such an extra at different milestones, in order to minimize confusion during play.
- An extra’s aspect can change at any minor milestone, or at a major milestone if it’s tied into your high concept.
- An extra’s skill may advance at any significant or major milestone, provided the move is legal, and you can get new ones at those milestones as well. You can also swap skill ranks between another skill and your extra at a minor milestone, like any other skill.
- An extra’s stunt may advance at a major milestone when you get a refresh point. This might mean you add a new stunt effect to an existing extra or buy a new stunt-based extra. You can also change out a stunt-based extra at a minor milestone, like you can with any other stunt.