YOu have this acquaintenance that says why?...after everything you say...?

When people have an annoying repetitive habit like that, I confront them when they are doing it and ask them why. Sometimes I might suggest an answer for them. Example: "Why do you need to ask 'why' after everything I say? Is it because you can't think of anything else to contribute to the conversation?" If the person doesn't realize they are doing it, this brings it to their attention and makes them ask themselves why they do what they do. If they do realize they are doing it, it helps them realize how annoying it is.

My five year old cousin does the same thing it drives me nuts

You could do like psycho-analysts do, and re-phrase her own question back at her. Say, "I don't know. Why do you think that is?" And don't say it in a smart-aleck way...say it seriously, so that when she takes the time to think about it, she'll realize what a stupid question it is.

Beat her at her own game........

I also have a female co-worker that behaves like that, and it bothers me a lot. Sorry, I don't have a solution for you because I totally have ignored her.