Crossword Genius

A petty offence at most excuses law’s harshness (8)

Ross

I believe the answer is:

acrimony

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'harshness' is the definition.
(thesaurus)

'a petty offence at most excuses law's' is the wordplay.
I cannot really understand how this works, but
'a' is within the answer.
'at' could be 'on' (location) and 'on' is found within the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for acrimony that I've seen before include "Acronym I made out of bitterness" , "Bitterness, ill feeling" , "Bitterness of manner or words" , "poison" , "Rancour, bad blood" .)

I've seen this clue in The Hindu.
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