I can only answer for Egypt but as far as I know Egypt is somewhat unique for the prevalence of full sibling marriage (as distinguished from marriage between half-siblings and first cousins).

To begin with we have to talk about how common this practice was using available demographic data, what this means according to scientific theories regarding deleterious recessive genes and the risk of mortality/disability, and what the evidence for negative effects is in ancient Egypt. I do not have the comprehensive answer for all 3,000 years of Egyptian history but since Roman Egypt is the most well documented time frame for the practice thanks to the regions where most of our surviving censuses come from, that is what I will focus on. Actually it is worth mentioning that it has been occasionally suggested that the practice saw a marked increase in the first two and a half centuries of Roman rule but we can not actually be sure of this.

Most estimates of full or half sibling marriage in Roman Egypt place it tentatively around an average of 20% of total marriages at any given time. This means that 1 in 5 couples were full siblings but there were also first cousin and uncle/niece pairings that we cannot account for which further complicate the degree of inbreeding. Combine this with the fact that the surviving evidence does not allow us to trace genealogies back more than 2-3 generations at best and we have no way to know how long this practice ran in families, a sibling couple may have had related parents but unrelated grandparents, an unrelated couple might have had full sibling parents and grandparents although they and their children married outside the family, and so on in even more complicated combinations.

Walter Scheidel in Brother-Sister Marriage in Roman Egypt, has concluded that given the underlying rate of infant mortality against fertility only 40% of couples would have had both a son and a daughter that could be married together, this is further reduced to 20% once it is taken to account that these unions were generally restricted to matches between an older brother and younger sister.

When it comes to the harmful effects of inbreeding on a population we should also establish a basic understanding of its causes and effects. First of all, inbreeding does not directly cause defects, but it multiplies the statistical risk based on factors like the closeness of the kin, their overall health, the genetic diversity of the population as a whole and the amount of generations in which it occurred. Harmful recessive genes which present rarely and may cause elevated rates of defects and/mortality are made more likely by consanguineous unions whose offspring are more likely to carry and express these genes, over time however there is a chance that these genes would be overall reduced or eliminated thanks to more individuals carrying these genes failing to reproduce. Basically populations have certain harmful genes waiting to cause problems for people when they crop up unexpectedly in generations, with predominantly exogamous unions the odds of harmful traits cropping up is low, with occasional inbreeding it increases in prevalence but does not significantly impact the odds of these genes getting passed down leading to increased overall risk, with sustained inbreeding over successive generations it is theorised to lead to a sharp increase mortality but the long term reduction of recessive traits in the general population and this has been observed in some animals as well.

Most estimates of incestuous marriage are taken from modern populations, especially in Asia and may therefore not be applicable to ancient Egypt which may well have had fewer harmful recessive traits (or more).

In Roman Egypt we then have two primary factors that would reduce the visible impact of associated defects and mortality, the likelihood of generational inbreeding and the already dramatically elevated rate of infant mortality which is usually placed around 30%. Since the increased risk of infant mortality and decreased fertility in modern populations as a direct result of consanguineous marriages is generally less than 5% and census data from Roman Egypt does not show significantly elevated infant mortality or lowered fertility in sibling couples there was not a debilitating or striking rate of defects. As I understand it, the risk of miscarriage and stillbirth is also elevated in consanguineous couples but the nature of the issue makes identifying links to genetic defects or the effects of inbreeding more difficult.

So although there would certainly have been some increase in risk for defects and morbidity it would not necessarily have been significant overall.

Given the nature of infant mortality as a fact of life in premodern societies, there is no reason to think that a trend of slightly increased risks would have been apparent, because the vast majority of people would have been unaffected and consequences might not emerge for a few generations making the causal link less apparent in the short run. Then it is important to note that the rationalisation of disease was different in the ancient world than it is today, individual cases of handicap and illness would not have been attributed to the genetic closeness of your parents or their parents, but to more immediate factors like environment, diet and the presence of harmful substances or even spiritual factors. Medicine in the ancient Mediterranean was all about balance, from what you ate to how you went about your life achieving a balance of substances and states on a physical and spiritual level was one of the most important keys to total wellness. Symbolic cures ranging from medicinal ingredients seen as being representative of certain traits or conditions to votive offerings were known, and the common use of protective charms, prayers and dedications to deities linked to health and children indicates that the cultural anxiety around the survivability of the very young was present but was expressed in different forms.

Beyond this, the big killer of infants, adolescents and adults was acute disease particularly infections, so chronic disorders were far less prevalent and worrisome. Developmental defects were also not entirely attributable to inbreeding, as malnutrition and stunted growth are evidenced in ancient societies far more frequently than developmental disorders obviously linked to genetic defects. This means that genetic disorders, much like many disorders linked to aging and cardiovascular disease, were not as statistically probable or lethal as they are today so even allowing an equivalent risk of genetic defects among ancient Egyptian populations as those noted today would mean that the odds of a person dying or being debilitated thanks to recessive genetic disorders would be negligible compared to the likelihood of succumbing to other ailments.

Sources

The Demography of Roman Egypt by Roger S. Bagnall and Bruce Frier

Brother-Sister Marriage in Roman Egypt by Keith Hopkins

Age and Health in Roman Egypt and Brother-Sister Marriage in Roman Egypt Walter Scheidel

The impact of consanguinity on neonatal and infant health by Alan H. Bittles and Michael L. Black

Women in Ancient Egypt by Gay Robin