Reading up on inbreeding depression and deleterious recessive alleles, I happened across a reference to a 1997 paper by W. Scheidel:
Brother-sister marriage in Roman Egypt
According to official census returns from Roman Egypt (first to third centuries CE) preserved on papyrus, 23.5% of all documented marriages in the Arsinoites district in the Fayum (n = 102) were between brothers and sisters. In the second century CE, the rates were 37% in the city of Arsinoe and 18.9% in the surrounding villages. Documented pedigrees suggest a minimum mean level of inbreeding equivalent to a coefficient of inbreeding of 0.0975 in second century CE Arsinoe. Undocumented sources of inbreeding and an estimate based on the frequency of close-kin unions (corrected downwards to 30% for Arsinoe) indicate a mean coefficient of inbreeding of F = 0.15-0.20 in Arsinoe and of F = 0.10-0.15 in the villages at the end of the second century CE. These values are several times as high as any other documented levels of inbreeding. A schematic estimate of inbreeding depression in the offspring of full sibling couples indicates that fertility in these families had to be 20-50% above average to attain reproduction at replacement level. In the absence of information on the amount of genetic load in this population, this estimate may be too high.
There is a substantial anthropological literature on the topic of brother-sister marriage in Roman Egypt, because it constitutes the most important documented exception to the incest taboo, considered a "cultural universal" in humans. There are other, more localized exceptions, but Roman-era Egyptians did not limit this kind of inbreeding to any small group (like monarchs or aristrocrats), but spread it across social classes. A 1996 paper by Seymour Parker gives a more comprehensive review. He concludes by discussing what the Roman Egypt example may contribute to our understanding of the "cultural universal":
We now approach a more difficult and murky issue: What does the present stud of brother-sister marriage tell us about the role of the incest taboo in human evolution?
Parker discusses the various complications with saying anything at all about human evolution on this basis -- most important, that the conditions under which the incest taboo may have evolved (either in hominids or earlier creatures) are not necessarily present in any recent complex societies, so the genetic or ancient cultural importance of the incest taboo may be quite removed from its present cultural importance. He concludes:
However, we can say with confidence that the Roman Egypt case shows that contrary to the implications of the various speculative theories on the functions of the incest taboo, this society existed for a few hundred years in its absence. There is not a single mention in the evidence that links sibling marriage to negative genetic effects or unhappy marriages. Finally, the very unusualness of this marital institution underlines the plasticity of human nature (Parker 1996:373-374).
Diocletian apparently ended the practice.
Parker S. 1996. Full brother-sister marriage in Roman Egypt: Another look. Cultural Anthropology 11:362-376. JSTOR
Scheidel W. 1997. Brother-sister marriage in Roman Egypt. J Biosoc Sci 29:361-371. Abstract