I'v been reading through the DH 2.0 book because my group is planing on starting a game after our current Numenera party gets killed. I do like the idea of Influence and Requisition test as it reduces alot of the book work in managing each player's current currency amounts and figuring out how to divide looted and rewarded currency.

However, the min issue I see is there is no system set up for selling items. There is a way to trade in a rarer item for something less rare, but no indication of what to do with old and outdated gear. At some point a character will want to sell off his starting Autopistol for a Hand Cannon or upgrade his flak armor to carapace armor.

Any suggestions for how to handle selling items?

I'd say give a bonus on the Influence check depending on the rarity of the item in question.

They can just as easily keep the gear, no problem in having a backup.