With due respect I would like to add a little bit more. I am a molecular microbiologist and have studied genetics quite bit and still going on with that. Cousin marriages do have a consequence in one condition, when there is a family inherited disease. As one might know, the life starts from mating of two separate genes, one from father and the other from mother. The genes have copies imprinted for the offspring. In most of the cases, nature selects the best one to be dominant/expressed, both copies align together and there are crossing overs going on that make up the genetic map of the offspring.
Now, if there is a same copy of a gene (lets say for example, hemophilia, a blood inherited disease) on both persons, it doesn't matter which passes on to the next generation. The result would be the same. Either combination will have the gene for that particular trait (in this case hemophilia). But if there is a different gene on the other person, preferably the superior/healthy one will be maintained. That doesn't mean necessarily that genes are wiped out, they stay there in the chromosome/genetic makeup but only as an inferior copy (which is not translated and stays silent while the superior gene is expressed/dominant). That inferior gene can still make a comeback when by chance it gets a similar copy in the next generation, which is still possible.
In humans and higher animals, as i can remember, every person carries two copies of a gene or chromosome and crossing overs are mostly random between the genes (thats what science knows uptill now), still there are definite points in the genes where crossing over is supposed to take place, so its not totally random.
As for example in case of blood group selection, suppose father is A then he is AA (two copies of same gene), and if mother is AB, that means she is AB (a copy of A gene and another copy of B gene, both are equally present)
and offspring can be with four combinations
A (father)+ A (mother) = AA = blood group A
A (father)+ B (mother) = AB = blood group AB
A (father) + A (mother ) = AA = blood group AA
A (father) + B (mother ) = AB = blood group AB
but if father and mother both are blood group A, so a combination of AA and AA will always be A. Similar things happen when other genes are selected during crossovers.
M. Irfan Arif
Groningen, The Netherlands