On what basis do Christians oppose cousin marriage?

I admit the question is a bit broad, so let me explain: In many cultures around the world, marriage of first cousins is common. However, the Catholic Church disallows marriage of first cousins (in absence of a special dispensation), and according to Wikipedia , this canon rule has a bit of a convoluted history. On the Protestant side, Luther and Calvin rejected this rule of the Catholic Church on the grounds that it is not Biblically based. However, I have met many Protestants who are anti-cousin marriage, and the general sentiment in American culture is that cousin marriage is morally wrong. I'm curious what the basis of forbidding or being morally opposed to cousin marriage is, within Christian traditions (though opposition to cousin marriage is obviously not universal). How did this idea originate, and is the same logic still applied?