Let's (try to) end the debate: Does biweekly mean twice a week or twice a month?

A dictionary search for biweekly likely won't clear up confusion about how often a biweekly meeting is being held. 

Merriam-Webster, Dictionary.com, and the Cambridge Dictionary each offer two different definitions for the adjective: occurring twice a week or occurring every two weeks. The language conundrum goes beyond biweekly; bimonthly and biannual also have competing definitions. Is the bimonthly meeting twice a month or is it every two months? Is the biannual family reunion twice a year or once every two years? 

The different definitions have left people — even the ones working at dictionaries — scratching their heads for a long time.