prepositions - "I've been doing this (for) a week" -- When do you leave out the 'for' when talking about duration, and when do you not?

The other day I heard someone say:

They've been going out a week; I mean, that's not (a) serious (relationship).

I wondered if she was speaking correctly, which is presumable, since she was a native American English speaker. But more often I here the for when people talk about duration. So is it also possible to leave out for? Maybe only in the informal register?

EDIT: There was a heavy stress on the word week. Does it play a role in this matter?

EDIT#2: ... OK. It's more suitable as an answer.