1st cousins are legal to marry in new York,
However it is very clear that generic diseases are more common when cousins marry than not. A perfect example is hemophilia which is genetic, Somehow Queen Victoria of England was a carrier and her children, grand children and great-grandchildren all were carriers. She was also the matriach of many of the European Dynasties of the 19th and 20th centry including Germany and Russia . Czar Nikolai was a grandson and Czarina Alexandra was also a grandaughter of Queen Victoria and they had a son with Hemophilia that likely helped bring down the Romanov Dynasty.
Genetic diseases are also more common among Amish who tend to marry cousins as well