The most common and most likely answer to this crossword clue is the 7 letter word THREADY
I've seen this crossword clue in The Times
T
H
R
E
A
D
Y
More clues leading to the result THREADY
Buddy explains!

The straight part
We know that "Weak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weak = thready.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 THREADY mean?
THREADY adjective- Of, resembling, or capable of forming a thread; filamentous.
- (of a pulse) weak.