To be clear, what we mean when we say it's okay for cousins to marry is actually that it's okay for cousins to sleep together. There are no real "health risks" posed by a piece of paper. Really, this is about sexual intercourse.
Here's a little truth bomb for you: More than 10% of people worldwide are married to a second cousin or closer.
In his book Consanguinity and Context (Cambridge University Press, May 2012), medical geneticist and author Alan H. Bittles examines the common misconceptions about cousin marriage from legal, cultural, religious and medical perspectives.
The Western world is generally scornful of cousin marriage, and in much of the U.S. it is outlawed entirely. Mostly, this taboo has to do with the risk of genetic abnormalities that is increased in babies whose parents are also cousins.
But, Bittles argues, based on his 35 years of research, we are all being a little paranoid. Yes, children whose parents are close biological relatives are certainly at a greater than average risk—studies of cousin marriage (and mating) worldwide suggest their risk of illness and early death is between 3 and 4% greater—but the risk only really applies in an appreciable way when the two married relatives who are both carriers of a disorder that is normally very, very rare—fewer than 10% of all cousin couples. Bittles argues also that studies of cousin couples fail to account for non-genetic factors on infant health: maternal diet during pregnancy, infection, socioeconomic status.
The upshot of procreating with a close relative is that disease genes are exposed and removed from the gene pool––a phenomenon called "purging." Purging, in early human populations would have kept genetic disease at a minimum, thus strengthening the tribe.
Today, with our modern ease of mobility and and shrinking family sizes, fewer close cousins are marrying than ever before. And that number will only continue to shrink, says Bittles, meaning less purging and more chance for genetic disease.