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I don't know the answer to your question but, and I hope the mods will allow it to remain, I do want to address how common both child marriages and early teen ages at first childbirth actually were, because they weren't anywhere near as common as time you seem to think in the medieval period.
Looking at the data for Tuscany during the early 15th century, we find 26% of all marriages taking place below the age of 16 in the cities, and 11% of marriages taking place below the age of 16 in the countryside, with the average age of marriage being 18.86 and 19.26, respectively. 3% of the marriages in the cities took place at the age of 13, and 7% at the age of 14. In rural areas, only 1% and 3% of marriages had a bride aged 13 and 14 years old. Significantly, Florence had the largest age gap between bride and groom (11.99 years, with the next highest age gap being 9.48).
Now, you may wonder why I say that child marriage wasn't common in the medieval period, given the high proportion of 13 and 14 year old brides in Tuscan cities, but I'm going to come back to that in a moment. For now, I want to examine the age at which women first gave birth. Unfortunately my source on Tuscan families (David Herlihy's Tuscans and Their Families: A Study of the Florentine Castato of 1427) either couldn't find sound enough data to calculate a women's age at first birth, but it does have some data on the ages of parents who had children born during the castato that is indicative: the mean age of a new mother in Florence was 27.13, with a standard deviation of 7.06, and the modal (most common) age was 20. The other cities and towns had slightly higher mean ages and SDs, and the mean age in the countryside was almost 30. The modal age was also a uniform 30 for all areas bar Florence. This data indicates that most women in Florence had children between the ages of 20 and 34, with those in other cities, towns and the countryside mostly having children slightly later. 32% of births still occured outside of this range, but given the risks associated with young childbirth I would suspect that relatively few girls under the age of 16 gave birth, though those who did probably had the largest age gap between them and their husband, as is common in India today.
Now, to bring this back around full circle, the average age of marriage for the noblewomen in England and France during the middle ages, though varying from region to region, was above the 20 year mark (J.C. Russell, Late Ancient and Medieval Populations; for a more recent study of English landowners, see H.E. Hallam Age at First Marriage and Age at Death in the Lincolnshire Fenland,). This is even older than the average age of marriage for the rural areas of Tuscany, and is indicative of a later age of childbirth. Even in the English royal family, which had a much lower average age of marriage than Florence, only 10.4% of births were to mothers under 16. This does not necessarily mean that men weren't having sex with their young brides, even before they reached the age of menarche (which was probably between 13 and 15 for the wealthy: J. B. Post (1971) Ages at menarche and menopause: Some mediaeval authorities), but the fact that in Florence children were typically born several years after the average age of marriage does suggest that there was minimal sexual contact with young brides. The English royal family shows a similar trend.
Based on the Western European Marriage Pattern, the average age of marriage in most of Western Europe was likely similad to England and France, which indicates that child marriages and young teens giving birth were likely uncommon.
Obviously, this is a complicated question. Your answer may vary widely depending on location, what the society or culture in question sees as sexualization, and how said society defines and delimits childhood/adulthood.
Rather than attempting a broad, global answer, let's take the United States as an example. Broadly speaking, in the 19th c. and earlier the "appropriate" age for marriage, sexual relations, labor - and other markers of adulthood - varied to an extent depending on your class and location. If your family was wealthy, there was little need to rush adulthood. If you lived in a rural area, more children meant more potential labor on the farm. If you were poor and living in the city, your child begging or engaging in under-the-table labor might mean the difference between having enough to eat that week. As a result, while there were certainly moral and biological hard lines few crossed (no one would consider a nine year old ready for adulthood), there tended to be more "give" in what constituted adulthood - and therefore, more fuzziness over who (and by whom) could be sexualized. A wealthy man from the city lusting after a fourteen year old, for example, would be egregiously immoral - such an interest would be obviously perverse, given the social mores in which he lived. But an eighteen or nineteen year old farmhand lusting after a fifteen or sixteen year old out in the boonies? Well, you gotta start a family sometime so you can have more laborers!
This is a generalization, but the point is that sexualization has historically been dependent on the realities of the space in which one lives. This becomes more evident when we factor issues of race and nationalism in - black slaves in the U.S. were often depicted and described as hyper-sexual, prone to engaging in sexual activity at a younger age, and more often, than their white counterparts. By describing slaves thusly, slaveowners dehumanized them while also creating a conception of what was "acceptable" and what was not. This ended up creating a kind of self-reinforcing feedback loop - if slaves were inherently, biologically more sexual, then it was more acceptable to sexualize them or engage them sexually - even at an age that one might consider otherwise reprehensible. Similarly, male U.S. travelers to regions like Central America or the Caribbean often felt far more free to sexualize younger girls (13-15) abroad in travelogues and diaries than they might at home - the lack of familiar social/cultural markers of American childhood and adulthood suggested to such travelers that non-white, "uncivilized" societies lacked such a division, and that age existed to such people as more of a spectrum than a quantifiable definition. Responses to sexualization of such young women (and sometimes men) might therefore be more forgiving.
By the turn of the 20th c., the end of slavery, Progressive Era idealism - which saw society as fixable through reform and regulation - as well as the decreasing isolation between American urban and rural areas, thanks to communication and transport technologies - were encouraging harder, and higher, limits on who was unacceptable to be sexualized across the board. California, for example, passed laws against the performance of a "lewd act" on a child under fourteen (1901), sending a minor to an immoral place (1905), performing degrading, lewd, or immoral acts in front of a child (1907), and contributing to a child's delinquency (1915). In 1929, California courts criminalized loitering near school yards and child molestation even more broadly. Such legislation did not emerge out of thin air - it was the effects of a society who increasingly saw child protection and definition of its duty, and who saw legislative power as the means to enforce what - or who - was considered acceptable and unacceptable. It is little surprise that such laws largely impacted (and were designed to impact) immigrants and poor/non-white Americans who either entered the country with alternative definitions of what was appropriate based on their cultures of origin, or who came from groups that had historically been designated as sexually perverse and uncontrollable. By creating - and raising - ages of consent, and enforcing social exclusion of those who did not conform to "proper" perspectives on who was acceptable to sexualize, such laws allowed for the those who did not know of, or follow, such standards to be ostracized and locked away.
Of course, this answer does not factor in issues of gender - which I will try to get to in a later edit. But I hope this does answer part of your question - when and how and why a shift in the acceptability of the sexualization of a particular age might occur.
(In case I don't get a chance to add to this answer, Nayan Shah's "Stranger Intimacy" provides some excellent analysis of gender in relation to the sexualization of youth in America.)
Ok people,
let me make a few things very, very clear here:
This question is a valid historical questions that is absolutely valid to ask about here. This is AskHistorians after all and the field of sexual and gender history are very interesting and great fields.
What will not fly here is just trotting out isolated historical examples of children being taken as lovers without providing historical context and fitting them in overarching historical narrative or any other sort of stuff that makes a low or no effort to answer the question within our rules. As our rules so clearly state:
Answers in this subreddit are expected to be of a level that historians would provide: comprehensive and informative. As such, all answers will be assessed against the standards of Historiography and Historical Method. You should cite or quote sources where possible. A good answer will go further than a simple short sentence. As described here, "good answers aren't good just because they are right – they are good because they explain. In your answers, you should seek not just to be right, but to explain."
And one other thing that will absolutely not fly here is either jokes about child rape, hurling insults at OP, or this weird age of consent lawyering that has popped up. This is a historical discussion, not one about the age of consent in the current day US or any other modern-day country. If you can't keep the discussion historical, don't post here.
This is your one time warning. Not heeding it will be met with the appropriate consequences.