Mostly I'm just arguing that it's ambiguous. I don't have a strong opinion, but the person I was responding to did and it seems like a silly thing to be so adamant about.
I'm 'so adamant' about what they mean only in the same sense that I am about any other word I know the meaning of, I only meant to be helpful.
For your bicycle example that I didn't reply to initially - I don't see what it breaks? Unicycles have one and tricycles three wheels. If i give you a wheel triweekly you have three by the end of the week and can build a tricycle.
FWIW, regarding correct usage: the dictionary on my computer (Oxford American English) lists both meanings of biweekly and does not put either meaning forward as more correct. It even has a whole entry on the ambiguity of the 'bi' prefix.
