We've no petty grievances with this set of collocations from Tim Bowen.
The adjective petty (derived from the French word petit, meaning small) has three basic meanings: trivial (not important and not worth worrying about), minor and mean/small-minded (when being unpleasant to someone). With the first two meanings, petty collocates with a relatively small number of nouns.
In the sense of trivial, one can find petty arguments, petty squabbles, petty disagreements and petty jealousies, as in 'I’m not interested in their petty squabbles’ and ‘Village life is full of petty jealousies’. In the same sense, petty can also go with grievances and complaints, as in ‘He quickly grew tired of people coming to him with their petty grievances’.
In the sense of minor, while one can talk about minor crime, the term petty crime is often used to talk about crimes that are not particularly serious, as in ‘The government has announced new measures to combat petty crime including vandalism, graffiti and litter.' The perpetrators of such crimes are petty criminals or petty offenders. A petty thief is one who steals items of relatively low value. Pickpockets are examples of petty thieves. In offices and other businesses, money kept for small, everyday expenses is petty cash (often kept in a petty cashbox), and a low-ranking officer in the navy is a petty officer.
With the meaning of mean or small-minded, petty collocates with the word remark as in, ‘She was hurt by his petty remarks’ and with the words behaviour and attitude, as in ‘They were upset by their neighbours’ petty behaviour and attitude’.