Looking briefly at the laws, the rationale behind the bans is often genetic: having low genetic variability increases the risk of children having genetic disorders, and the risk to children of cousins is about twice as high as for unrelated parents.
Something to consider: if the rationale for banning first-cousin marriages is to reduce the risk of children being born with genetic disorders, why does such a ban not extend to parents with genetically-inherited diseases?
Of the long list of genetic disorders, many are recessive (including cystic fibrosis and sickle-cell anemia). This means that two parents with a recessive genetic disorder getting married have far increased risk of passing on their disorder than parents for whom only one partner has the gene. Does the argument against cousins getting married necessarily extend to these potential parents?
How do we feel about banning marriage between cousins, but not between parents with sickle-cell anemia? Is there a difference, and if so, what is it?
Bonus Considerate points: do the same arguments apply to siblings marrying?