If I have a Kaisa at a bf with a Back Off hidden, on the next turn my opponent plays a spell to increase the might of the Jayce in the base. Can I react now with Back Off on the Jayce in base?

No. A hidden Back Off can only choose a target at the battlefield where it was hidden — Jayce is in base, so he isn't a legal target (Rule 811.1.d.2).

Timing isn't the problem: since Back Off was hidden on a previous turn, it gained [Reaction] and you can play it in response to your opponent's spell. But when played from Hidden, its "Stun a unit" target must be chosen from among options at that same battlefield, and Back Off has no targeting text that would free it from that restriction. If you want to hit a Jayce in base, you'd have to play Back Off normally from hand instead.