You do not tell how weak is weak. 2 or 5 frames?
If you give to that size hive a new queen, it is not able to much.
3 frame hive should be restricted to 3 frame space. Otherwise it cannot keep brood area warm.
Even if a colony seems to use 3 frame, they may be on upper parts of frames and actually they have one frame of bees.
*** you may handle your weak hive with thymol to kill possible travhea mites and varroas.
Then pour to bees syrup into combs that they fill themselves with syrup.
Then join colonies without newspaper.
When you put colonies to a langstroth box, you may take a frame of emerging bees from your best hive that you get a box totally filled.
Then the colony is ready to make winterbees. The winter cluster will be same size as brood area at the end of season.