Language evolves perpetually. My suspicion is that
two times has come into British English from the US where immigrants of German origin translated directly from the German
zweimal to give
two times in English, where a Briton would have used
twice. The point of entry was perhaps expressions such as
two-time champion,
two-time killer or simply
two-timer where the theoretical British equivalents of
twice champion,
twice killer and
twicer do not really sit happily in English phonology (the oral sound system). A similar thing may have happened with form filling. Britons have traditionally
filled in a form. US usage has long been
fill out a form; which would be a direct translation of the German
ausfüllen,
fill out. Around 50 million US citizens claim German ancestry and German was widely spoken there in areas of heavy German immigration up until the First World War, following which its popularity as a public spoken language declined. These linguistic curiosities may well be traces of that era.
Having said all that, go to the
OED (Oxford English Dictionary) website if you really want to know — etymology (word origins) is a notoriously nuanced subject and what is apparently obvious often proves to be completely wrong.