The most common and most likely answer to this crossword clue is the 9 letter word IMPOTENCE
I've seen this crossword clue in Financial Times
I
M
P
O
T
E
N
C
E
More clues leading to the result IMPOTENCE
Buddy explains!

The straight part
We know that "weakness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weakness = impotence.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does IMPOTENCE mean?
IMPOTENCE noun- Powerlessness; incapacity.
- Inability to copulate or beget children; sterility, erectile dysfunction, etc.