Well, if you can't afford to devote equal time to both, then what it'll basically come down to is either that the weakness is quick and easy to discover, but difficult to obtain, or that it's difficult to discover, but quick and easy to obtain.
So, it's either like Superman, where everyone knows he's vulnerable to Kryptonite but finding some is very difficult, or it's something like a food allergy - a very closely guarded secret, but once you know about it you've basically just got to grab a few gallons of peanut butter.