I guess petty characters are interesting because they usually help create situations for other characters that other way wouldn't exist. Something that would go without much of a call might be the cause of a petty grudge or obsession and will move this character to put the protagonist into a new direction that might invigorate things or move the plot into a different direction.
Not every character has to be relatable and sometimes having characters that are so cringy and petty gives us something to focus our negative feelings without guilt. Many people hope for them to get their just desserts and anticipate such moments.