Fortnight and fornightly are both familiar words to any English speaker. However the terms are less commonly used in the USA than other English speaking countries. I once had a discussion with an American about this very term and the person indicated that some friends did not know the word.

The term is long standing in the English language and literally meant 14 nights. So two weeks or fourteen nights, take your pick.

I don't know why it means 'two weeks'. It'ss just the way the language developed, just like how in Chinese you can say 前天 instad of 两个天前 and 后天 instead of 两个天后.

It's definitely very common, especially when describing a frequency (ex. "I get paid once a fortnight).