How distant of a cousin is she to him? Cause if it's like 5th, then it's totally ok. A lot of people marry their 5th cousins without even knowing and everything is fine, no deformed children, nothing. You might be married to one right now.
The risk of birth defects even between First Cousins is much lower than you think. The caveat is that you don't want to make a family tradition of marrying close cousins. That's when you get the Hapsburgs.
For simple same-generation relationships the fraction of DNA shared is 1/(2^R) where R is degree of relation (sibling = 1, first cousin = 2, etc).
Go ahead, marry your cousin—it’s not that bad for your future kids
In biology, genetic diversity is all the rage. If something goes wrong with the genetic material provided to you by your mom, you’re more likely to shake it off if your dad’s genetic material is very different. If dad’s left you hanging when it comes to susceptibility to a certain disease, a mom from a radically different gene pool could confer the protection you require. If mom and dad are genetically similar, however, both versions of a gene are likely to shut down at the same time.
It’s estimated that 4 to 7 percent of children born from first-cousin marriages have birth defects, compared to 3 to 4 percent for children born from distantly related marriages.
That’s not nothing, but it’s also not the end of the world—or the family tree. The real issue would arise if the next generation of kids also married their first cousins. Their offspring will have even more DNA in common—and an even greater chance for birth defects.
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Ultimately, marrying your first cousin carries some risk. But the odds of healthy offspring dramatically improve with each new distance of relation. Second cousins share only 6.25 percent of their genes and third cousins share just over 3 percent. Seventh cousins—the average distance between modern American spouses—have no meaningful genetic relation at all.