The most common and most likely answer to this crossword clue is the 14 letter word COUNTERBALANCE
I've seen this crossword clue in The Sunday Telegraph
C
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Buddy explains!
The straight part
We know that "Apply equal weight against" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case apply equal weight against = counterbalance.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 COUNTERBALANCE mean?
COUNTERBALANCE noun- A weight that is put in opposition to an equal weight so it keeps that in balance.
- A force or influence that balances, checks or limits an opposite one.
- To apply weight in order to balance an opposing weight.
- To match or equal in effect when applying opposing force