For me, a woman, it is very common to go out together with a woman as a friend. In the case a person is male, however, I hesitate to go out with just the two of us...as far as my experience, we Japanese tend to avoid to go out with people who are opposite sex (as a friend). It seems true among the aged Japanese.
I wouldn't think it was weird. I'd think you were trying to con a free meal or movie out of me though (For some reason it's considered rude to ask the woman to pay for their own share). In most cultures, for some stupid reason, it's tradition for the male to ask the woman out.
... I can't think of any pragmatic or scientific reason for this, however, scientifically most traditions are an idiot thing anyway.