Relatives by marriage (in-laws) are called affines and to marry an affine was to violate the Catholic Church's prohibitions against marriages between affines. Some ancient legal systems did not recognise affinity as a problem for marriage. For example, the early civil law of Rome placed no restriction on the marriage of affines. However, this changed with the Empire's conversion to Christianity. Some three centuries after Rome's conversion to Christianity, Justinian ordered an ambitious codification of the civil law. In the Institutes, which served as a textbook in the Roman schools of law, we can read what was the contemporary opinion on affinity:

Certain marriages again are prohibited on the ground of affinity, or the tie between a man or his wife and the kin of the other respectively. For instance, a man may not marry his wife’s daughter or his son’s wife, for both are to him in the position of daughters. By wife’s daughter or son’s wife we must be understood to mean* persons who have been thus related* to us; for if a woman is still your daughter-in-law, that is, is still married to your son, you cannot marry her for another reason, namely, because she cannot be the wife of two persons at once. So too if a woman is still your stepdaughter, that is, if her mother is still married to you, you cannot marry her for the same reason, namely, because a man cannot have two wives at the same time (1.10.6).

This prohibits marriage to a stepdaughter and a daughter-in-law on the basis that they are, properly speaking, daughters. So the Roman law arrived at this prohibition via a conflation of consanguinity and affinity. Indeed, affinity was persistent enough to last into perpetuity, as can be inferred from the emphasised text above and the prohibition against one's marrying a stepmother or mother-in-law:

it is forbidden for a man to marry his wife’s mother or his father’s wife, because to him they are in the position of a mother, though in this case too our statement applies only after the relationship has finally terminated (1.10.7).

So there is one line of reasoning from around 650 AD. But was this a proper representation of the Christian line of reasoning?

There are some comments in well-known Christian documents on the issue of affinity. An obvious example is near-contemporary to the extracts above. It occurs in Bede's account of the conversion of England to Christianity when, in 595, Augustine, the first Archbishop of Canterbury, writes to Pope Saint Gregory to ask whether affines may marry, in specific reference to stepmothers. According to Bede, Gregory replied thus:

To marry with one's stepmother is a heinous crime, because it is written in the Law, “Thou shalt not uncover the nakedness of thy father:” [Lev. 18:7; Lev. 20:11] now the son, indeed, cannot uncover his father's nakedness; but in regard that it is written, “They twain shall be one flesh,” he that presumes to uncover the nakedness of his stepmother, who was one flesh with his father, certainly uncovers the nakedness of his father. It is also prohibited to marry with a sister-in-law, because by the former union she is become the brother's flesh [Mark 10:8]. For which thing also John the Baptist was beheaded, and obtained the crown of holy martyrdom [Matthew 14:1-12, Mark 6:14-29, Luke 9:7-9]. For, though he was not ordered to deny Christ, and it was not for confessing Christ that he was killed, yet inasmuch as the same Jesus Christ, our Lord, said, “I am the Truth,” because John was killed for the truth, he also shed his blood for Christ.

But forasmuch as there are many of the English, who, whilst they were still heathens, are said to have been joined in this unholy union, when they attain to the faith they are to be admonished to abstain, and be made to know that this is a grievous sin. Let them fear the dread judgement of God, lest, for the gratification of their carnal desires, they incur the torments of eternal punishment. Yet they are not on this account to be deprived of the Communion of the Body and Blood of Christ, lest they should seem to be punished for those things which they did through ignorance before they had received Baptism. For in these times the Holy Church chastises some things with zeal, and tolerates some in mercy, and is blind to some in her wisdom, and so, by forbearance and blindness often suppresses the evil that stands in her way. But all that come to the faith are to be admonished not to presume to do such things. And if any shall be guilty of them, they are to be excluded from the Communion of the Body and Blood of Christ. For as the offence is, in some measure, to be tolerated in those who did it through ignorance, so it is to be rigorously punished in those who do not fear to sin knowingly.

I have inserted Biblical references in square brackets in case you wish to read further, but I will try to explain the reasons here.

Gregory points out, firstly, that to marry one's stepmother violates prohibitions contained in Leviticus. His appeal is to the opening chapters of the Holiness code, which is dedicated to forbidding a great number of relationships. It's hard to get reasons from God's fire-and-brimestone instructions here, but a sexual relationship with one's stepmother is regarded as being punishable to the same degree as homosexual, bestial, and bigamous relationships. Sexual relationships with one's stepmother are punishable to a higher degree than relationships with one's sister-in-law (Lev. 20:21).

I imagine that Gregory would have cited cited scriptural authority on the wrongness of relationships with one's sister-in-law if Augustine had specified that kind of relationship in his question. I don't think Gregory was picking-and-choosing outlawed relationships from Leviticus. However, he does seem to be derogating from the punishments that Leviticus states are meant to be meted out for these sinful relationship. As we see in the second passage, Gregory holds that all is not lost for those who were once "heathens... joined in... unholy union". It is possible, though it cannot be inferred from this argument alone, that Gregory did not see a difference in severity between sexual relations with one's stepmother and with one's sister-in-law.

I think the interpretation is bolstered by his second argument. The second argument Gregory makes is simply that conflation of consanguinity and affinity which we saw earlier in the Institutes, except here it has scriptural basis. Since consanguinity is a grave sin that does not admit of shades of grey, it stands to reason that relationships in spite of affinity do not either, provided that they are the same crime.

Importantly, I note, the Catholic Church had outlawed consanguinity independently of the Roman law, and to a greater extent. The Council of Adge had achieved this in 506 AD by outlawing the marriage of first cousins. This was a more stringent restriction than that found in the civil law and shows both the weight the Church put on the crime and that you couldn't get around this line of attack by jurisdictional forum shopping.

A potential third reason is in the death of John the Baptist. In this story, King Herod marries Herodias, his sister-in-law, and has John the Baptist beheaded for speaking out against the marriage. One doesn't have to read this as a distinct argument, it could simply be that Gregory is furnishing an example of how old the tradition of interceding in marriages of affinity is. As a rhetorical flourish, however, it may constitute a distinct argument inasmuch as it evidences the depravity one might partake in to secure one's relationship of affinity - that is to say, you may wind up killing a future saint out of the desire to marry your brother's wife.

I'll leave that third one up to you, but want to dwell on the first two reasons, which are concrete. I want to dwell on these two because they were significant to a host of writers from the early period of Christian teaching.

I want to bring us much closer to your question about widows than the more general discussion of affinity has so far taken us. On this point, recall that the Institutes not only outlawed bigamous marriages of affinity, but also those with "persons who have thus been related to us... [even] after the relationship has finally terminated". Now notice how Gregory subtly makes this same point that one can never be free of the relationship of affinity irrespective of bigamy: "It is also prohibited to marry with a sister-in-law, because by the former union she is become the brother's flesh."

Though, as we have seen, the Catholic Church outlawed marriages to affines of all stripes, in these two excerpts the writing verges on an advocacy of widowhood. And an advocacy of widowhood is just what one finds in the writing of, say, Ambrose, who writes about this at length in Letter 63:

What virgin can hear without grieving that her chastity will have no reward? Far be it from her readily to give credence to this, still less let her lay aside her earnestness, or change the intention of her mind. What widow, were she to find her widowhood profitless, would choose to preserve inviolate her first marriage-vow, and live in sorrow, instead of allowing herself to be comforted? What wife is there who hearing that no honour is due to chastity, might not be tempted by unwatchful heedlessness of mind or body? And that is why the Church, in her sacred Lessons, in the discourses of her priests, daily sends forth the praises of chastity, the glory of virginity.

Consider that the only way a marriage of affinity could occur without being bigamous is if it involved a widow or widower, and we begin to see how intense the strictures were in the correspondences of the Church Fathers. For not only is engaging in such a relationship wrong, but desisting from the relationship is right.