Recently Gao et. al. published “An Estimate of the Average Number of Recessive Lethal Mutations Carried by Humans”. They studied a Hutterite group in South Dakota, highly inbred (63 founders 13 generations ago). From serious genetic diseases common in this population, they determine the number of deleterious variants present in the founders. They find that 0.29 recessive lethal alleles per haploid genome. Since some lethals manifest before birth, they double the estimate to 0.58.
This gives an expected 1.8% increased chance of a genetic disease from two first cousins.