Jim . K
Well, I am aware of that but it somehow does not feel right. I was thinking about replacing them with another random basic weakness or something like that. But on the other side I could put some roleplaying in and try to solve them even in standolone to achieve 'full win' without a bitter aftertaste of fail.
What you could do is:
Limit yourself to gaining any clues until you have repaid one (or more) clue to discard the weakness card. So it kind of becomes a staller to your progress. I think you would have enough clues available to do this from the locations, but if not, you could simply draw them from the pool when you investigate. I think it's well within the spirit of the game to give yourself some sort of setback/challenge to face in drawing your weakness.