I think the conflict is between invisibly different sub-word groupings. I think of them as “(biweek)ly” = “happens every biweek” = "happens every two weeks, vs. “Bi(weekly)” = “happens twice as much as weekly” = “happens two times every week”.

That doesn’t really help the ambiguity, so I prefer other ways of describing the recurrent timing of events when there isn’t anything obviously disambiguating them - for example, if I create a digital calendar event and name it “biweekly event”, the existence/nonexistence of repeated calendar events makes it obvious what is meant.