It can hurt more than a bit (4)

I believe the answer is:

bite

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This might be a double definition.

'it can hurt more than a' is the first definition.
The definition suggests a singular noun which matches the answer.

'bit' is the second definition.
(synonyms)

Can you help me to learn more?

(Other definitions for bite that I've seen before include "Small amount to eat" , "Morsel" , "Mouthful" , "Quick snack" , "Cut with the teeth" .)

I've seen this clue in the Evening Standard.

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