so you could use jairus to heal a warrior with a weapon and it would keep it?
Characters can be healed by a healing enhancement at any time during the turn, even after battle, and they retain all abilities gained prior to the discard. The REG specifies that cards placed on characters are kept when they are in Potter's Field, so I am assuming that is a standard default. I could be wrong however.
Jairus' ability may be used as soon as he enters battle. He could heal anyone discarded up to his entry, but not after. Also, any hero he brings back from the discard pile from a previous turn is not considered "healed." That character would enter play at face value, like a "search."