I think that multiple generations of cousin marriage causes a higher incidence of genetic disease. Take the Hapsburgs, the Romanovs, and all of the European royal families.
One incidence of first cousin marriage/ children in a family is not a problem, health-wise, and PP have pointed out statistics vs children born to women over 40. The children of one first cousin marriage are not automatically destined to suffer genetic or other diseases, as some posters on this thread seem to be saying.
My father's parents were cousins. My father and his brother are normal healthy individuals, and all of their children are likewise healthy.
I don't see how legislation could protect from multiple generation first cousin marriage without unnecessarily penalising one- off occurrences