The most common and most likely answer to this crossword clue is the 4 letter word PINE
P
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More clues leading to the result PINE
Buddy explains!

The straight part
We know that "Weaken" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weaken = pine.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 PINE mean?
PINE noun- Any coniferous tree of the genus Pinus.
- Any tree (usually coniferous) which resembles a member of this genus in some respect.
- The wood of this tree.
- (obsolete except South Africa) A pineapple.
- A painful longing.
- To languish; to lose flesh or wear away through distress.
- To long, to yearn so much that it causes suffering.
- To grieve or mourn for.
- To inflict pain upon; to torment.