Anyway is how you get back to the point. You start telling someone about the weekend, you get sidetracked into the delayed train and the terrible sandwich, and then — anyway, we finally arrived at nine.
It also means in spite of that: it was pouring and we went anyway. Put at the end of a sentence it waves the whole matter away — I didn't want to go anyway. Two words, any way, is something else entirely: do it any way you like. Anyways, with the s, is loose spoken English rather than the written form. And a long anyway, said while standing up, means the conversation is over.
1adverbanywayUsed to return to the main point after a digression.
“Anyway, as I was saying, the meeting has been moved to ten.”
2adverbspiteIn spite of what has just been said.
“The forecast was terrible but they set off anyway.”
3adverbaddUsed to add a reason showing that the matter did not really matter.
“Don't apologise about the ticket — I was busy that night anyway.”
Too few real examples of this word to estimate which sense is commonest.
Anyway is any and way welded together, and it once meant just that: in any way at all. The two-word any way still carries the older, literal sense, which is why the pair are so easy to muddle.
From any + way.
Etymology from Wiktionary, CC BY-SA