I wrote about this a few years ago:
I noticed a recent discussion which quoted a recent paper claiming significant damage to intelligence from cousin marriage as it is practised under modern conditions.
What has to be said is that cousin marriage practised under modern conditions where child mortality rates are just a few percent; is a completely different situation from cousin marriage practised under the situation prevalent among almost everybody throughout most of human history - when child mortality rates exceeded fifty percent.
When most children died, there was an extremely tough selective sieve, which would be expected to remove most children with genetic damage - more would be removed by differential deaths of young adults (especially of men) and sexual selection with assortative mating.
So, most of the problems of inbreeding, including cousin marriage - are likely to be an artefact of the almost-complete-removal of the most powerful selective mechanism operative on humans.
Conversely, the advantages of cousin marriage would have been relatively much greater - these advantages including better knowledge of partners, higher rates of social cooperation, and also the mutation-purging benefits of assortative mating - in that the lineages with the 'best' genes would tend to marry; while the left-over lineages, in which genetic damage was concentrated, would also marry and their damaged genes would tend to be eliminated from the gene pool.