Re: 2 New Colonies; 1 weak, 1 strong (need advice)
sounds like they think they have a queen, since they are not making queen cells on the frames you are introducing.
they probably have what i call a 'runt' queen, a small non-mated or poorly mated queen that isn't laying, but makes the colony think its queenright. these are very hard to spot especially for a beginner.
i had this happen in my first season, didn't realize it, and tried to introduce a bought queen which they ended up killing.
the way i figured it out was to take a queen excluder and put it on the bottom of the box. i then shook out all of the bees and let them fly back in. once they were in i removed the box, took the bottom board aside and removed the excluder.
i didn't see her at first as she wasn't much bigger than the workers. i noticed a few workers 'attending' to this one bee and when i looked close i could see that her abdomen was shaped a little differently. i decapitated her with my hive tool and more of the workers got interested in her.
i put the hive back together, gave them another queen, problem solved.
journaling the growth of a treatment free apiary started in 2010. 20+/- hives