strengthening small hive

Yes, of course you can. I would ask...How weak is the small hive? Will adding frames of brood resuscitate the weak colony? Is it worth weakening the strong colony in late September?

Yes you can. I moved some of my extra frames (deeps with honey in them) from a colony merge I did because they the colony was just way too large for the bees to cover during the winter. I have also moved brood frames earlier in the summer and they where accepted by the same colony.

Note I am a newbie myself so I'd defer to Mike Palmer first. ~Daniel