The simplest answer to this really is: same as we've always done. That's just how evolution works.
This unusual situation is because of a rare genetic abnormality that causes hyperovulation. In this fictional world, this is the norm rather than the exception.
A trait never spontaneously becomes widespread. One person bears a "rare genetic abnormality" that then becomes a recognised allele for a gene (or a combination of alleles for some given genes), which may or may not become dominant if it offers an enhanced physical trait, and the population is under selective pressure by its environment. So, if the trait ends up widepread, it's because it offers an advantage over the alternative. The risk/reward ratio has to be beneficial, or it would have never stuck in the population.
So your question should probably be formulated as "What would make the risk/reward ratio beneficial for this trait?"
Overpopulation would be a major issue in most parts of the world.
One birth in each mother's lifetime would suffice to create a generation at least as populous as its parental one. Even in today's world, there are many couples that opt to not have any children, or adopt. Perhaps earlier there would have been more ressource wars (and bloodier wars, seeing as many deaths would impact the populations less than ours did), but it would most likely even out.
In addition, every pregnancy is a risk to both mother and child before the modern world.
Evolution dictates that only women who can survive these extreme childbirth conditions will live on to generate more offspring, so the risk will stabilise at a level close to the one we know. In addition, modern medicine has greatly improves the safety of childbirth. Perhaps gynecology was the first specialist medical discipline to emerge.
Children who are multiples are usually born smaller than average in order to take up space in the womb.
Yes, but we are all born quite small. We all grow throughout childhood and puberty. Perhaps we would require some more care as infants and more nutrition growing up, but I doubt this would have any real effects on adults (if given an appropriate diet).
Our brains need to be large at birth in order to grow into the large adult brain. By shrinking the size of children, and therefore the size of the brain, it may have unforeseen consequences for us later.
Same as before, our brains grow after birth, so perhaps we would be useless babies for a little longer, but I don't expect it to have a massive impact.
All in all, I don't think there are very many risks associated with that trait, if managed properly. The rewards however could be quite interesting for an early, or even medieval, human society.
A quick sidenote on the societal aspect of this: Mariam the SuperMother is from Uganda, a country that is very Catholic in its beliefs, and like many of these countries of subsaharan Africa, sex education, contraceptives and sexual autonomy are often difficult to come by. I doubt that Mariam would have mothered 44 children if she had been born in Sweden for example. If the hyperovulation trait becomes widespread in your society, perhaps the religions would venerate a woman's bounteous loins more, and elevate them in society.