The most common and most likely answer to this crossword clue is the 6 letter word FOIBLE
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More clues leading to the result FOIBLE
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 = foible.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 FOIBLE mean?
FOIBLE noun- A quirk, idiosyncrasy, or mannerism; unusual habit or way (usage is typically plural), that is slightly strange or silly.
- A weakness or failing of character.
- Part of a sword between the middle and the point, weaker than the forte.
- Weak; feeble.