I recently answered a similar question which I am copy pasting most of this from.

This is actually a difficult question to deal with and many historians have tried their hand at it.

We can try to apply medical knowledge and theory but this is hampered by the availability of our sources. There are no medical records of the Ptolemies, and the ancient understanding of medicine and anatomy was radically different. The concepts of genetics, psychology, and congenital defects did not exist. Even if physicians had left us full medical histories for each generation of Ptolemaic dynasts, and they elaborated on any health issues they may have had, we might still be in the dark. The reason for this is that even things like the description and diagnosis of symptoms was radically different, and at times modern readers struggle to prove the existence of certain diseases based solely on literary evidence.

It is worth noting that inbreeding on its own does not cause genetic defects, it merely increases the likelihood of defects over time. Inbreeding allows for otherwise recessive alleles to express themselves as opposed to being covered by dominant genes. This means that a lack of genetic diversity lends itself to the appearance of recessive traits, including defects. In particular, elevated rates of infant mortality often occur in connection to inbreeding.

Additionally, it is worth pointing out that not every group or population would suffer the same way from inbreeding. Inbreeding among healthier individuals would mean that there is a good chance that issues would not emerge as quickly or be as severe. Inbreeding could hypothetically have had a positive effect on the Ptolemaic dynasty after an extended period. 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.

There is no guarantee that recessive defects have to emerge as a result of consanguineous unions, and it ultimately boils down to a combination of luck and the overall health of the individuals involved. The Ptolemids might have just been healthier than the Hapsburgs, or they might have just been luckier.

Different populations in both ancient and modern societies displayed different rates of elevated infant mortality and defects in connection to consanguinity. In fact, many regions have remarkably elevated rates of consanguineous marriage, with marriages between first cousins accounting for more than half of all marriages in modern nations like Qatar and Pakistan. For an ancient example, Roman Egypt is thought to have experienced an increase in sibling marriage from earlier time periods, with more than a fifth of documented marriages occurring between siblings. Despite this, the population of Egypt in the Roman period evidences rates of deleterious effects far below what is expected as a result of the high rates of sibling marriage, and we still do not know why this was (it might only seem this way because of the surviving evidence!)

Even in ancient Greece, marriages between relatives close enough to be considered incestuous today (cousins and uncles) were fairly common. At Athens and Macedon, marriages between paternal half siblings was even legal. In Rome, half siblings and uncles was considered too close, but first cousin marriage was not.

Inbreeding coefficients also multiply over generations which complicates things quite a bit, for instance Charles II has been estimated to have inbreeding coefficients comparable to a child born of a full sibling union.

In terms of the actual rates of inbreeding among the Ptolemids, it was not extensive enough that there is any scientific reason why we necessarily should have seen any defects. Sheila Ager in Familiarity Breeds: Incest and the Ptolemaic dynasty pointed out that in 250 years reign, the Ptolemaic dynasty did not experience 250 years of consanguinity. In fact, the first Ptolemaic king to be born from a full sibling union was Ptolemy V who married his distant relative, the Seleucid princess Cleopatra I. They married other dynasties like the Seleucids, they married individuals with foreign blood like Persian and Anatolian descent, there were even a few illegitimate Ptolemies of unimportant mothers. Even in cases of Ptolemaic inbreeding, many marriages were between second or third cousins which is fairly safe.

Despite what Wikipedia family trees indicate, their genealogy is not always clear, and with individuals like Ptolemy XII and Cleopatra VII we have no way of tracing their descent definitively. For instance, Ptolemy XII's mother is presumed to have been a concubine but she might well have been a close relative of his father, we just do not know for sure. Cleopatra's mother has been suggested to be either his brother's sister, a concubine, a minor wife from the Ptolemaic family or a partly Egyptian priestess by different scholars. It is technically possible that they could have suffered from the more severe ill-effects of inbreeding, it is equally possible that they did not.

Our only references to the health of the Ptolemids besides historical accounts come from artistic depictions of the Ptolemies. This comes with the caveat that it is not necessarily accurate. Sure Hellenistic art is often photo realistic, but that does not mean that it has to accurately reflect the appearance of its subject. The apparent heaviness and bulging features of certain Ptolemids have been pointed out as signs of some thyroid imbalance or hormonal issues but we can see these even on certain portraits of Ptolemy II and Arsinöe II who began the tradition of sibling marriage and were themselves not the product of incest. The large eyes of the Ptolemies can be traced back to Ptolemy I and Berenike’s coin portraits which points towards an iconographic tradition, rather than a pathology. Not to mention that statuary and paintings of the Ptolemids often do not feature these traits (like this bust of Ptolemy Apion ) and tend to vary wildly in general which makes sense because all of these portraits' were carefully crafted to convey certain symbolic meanings.

The majority of the Ptolemids seem to have been physically able and many were long-lived if they did not die of violent causes which seems to indicate that there were no debilitating or severe defects. That they had no issues with fertility is fairly clear, and even later Ptolemies like Ptolemy IX and Cleopatra VII were apparently healthy.

Ptolemy VIII was apparently morbidly obese and it could be argued that this was the result of the deleterious effects of inbreeding, but his parents were only third cousins which is well within safe boundaries and social norms in Hellenistic society. Beyond this, earlier generations of Ptolemids who were not the products of incest (like Ptolemy II and Arsinoë II) evidence a tendency towards heaviness.

Cleopatra was said to be charismatic and fairly attractive, with her only known illnesses or health issues being acute rather chronic diseases. She was evidently not infertile since she had four apparently healthy children who survived infancy (in and of itself a noteworthy achievement in Ptolemaic Egypt which saw infant mortality in excess of 30%) and possibly a miscarriage c. 44 BCE. So all in all, no apparent problems here. On the other hand, it is possible (if unlikely) that she struggled with unhealthy weight gain although the majority of portraits portray an apparently healthy woman. Historian Duane Roller interpreted an account of her not eating for an extended period as a possible attempt at weight loss rather than a manipulative ploy or an emotional issue. Furthermore, a Pompeiian portrait of a rather hefty queen committing suicide is sometimes suggested as Cleopatra although I personally find the evidence in favour of the previous interpretation of the painting as a portrayal of a certain Carthaginian queen. Overall, the majority of historical evidence suggests that she was plenty healthy although in truth, her rather energetic lifestyle and career probably did her no favours there.

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