I assume it is a standard bmx bb and not a cartridge bb.
The concept is the same as a headset,too tight and it will bind, too loose and it will wobble. You need to loosen the lock nut and adjust the cups, you can usually do this by hand, and is as you imagine, a really fine line, then tighten lock nut down onto cup.
I the headset was dry, shouldnt be, then worth checking the bb bearings, usually in cages but older ones used to be loose bearings, get plenty of grease in there

EDIT: just re-read the post, and my reply

meant to say, if the wheel bearings were dry, not headset, and the bb should be the same as the wheels you have already done, axle with bearings at each end and same way to adjust it.