Eh, I don't think she does so on purpose - she has feelings for him, obviously, and doesn't really know how to deal with them, because she knows that it's "wrong." So she hangs out with him, but can't quite master the art of doing it in a way that isn't... tinged with some degree of flirtatiousness, for lack of a better word, subconscious or not.

He's attracted to her too, on some level, and probably in denial about it (because he wants to be a good guy, and good guys don't fall for women who aren't their wives). What might pass as "hitting on her," were he single, is probably just harmless friendliness in his eyes. Which just makes the whole thing worse.