I do have a weak colony. Two frames of bees, it does have some brood so it seems queenrite. If there is no brood, I look for the queen. I know that it is too weak to be a honey producing colony. It may build up to a strong colony by August but it may be a liability if I have to feed it large amounts of syrup in late summer.
The best thing to do is bolster it with a 2 lb package of bees.
All I do is start the package in a box as normal. During this time hopefully the weak colony has got a little better. When it is time to add a second box to the package, sometime in May. I go into the weak colony a find the queen and dispose of her. The weak hive is then left queenless overnight. The next day a sheet of newspaper with a tiny slit in the paper is put on top of the package. The weak colony is then put on top of the package on the newspaper. The bees will slowly chew through the paper and unite the two colonies.