Objection 1. It would seem that a person does not contract affinity through the marriage of a blood-relation. For "the cause of a thing being so is yet more so." Now the wife is not connected with her husband's kindred except by reason of the husband. Since then she does not contract affinity with her husband, neither does she contract it with her husband's kindred.
Objection 2. Further, if certain things be separate from one another and something be connected with one of them, it does not follow that it is connected with the other. Now a person's blood relations are separate from one another. Therefore it does not follow, if a certain woman be married to a certain man, that she is therefore connected with all his kindred.
Objection 3. Further, relations result from certain things being united together. Now the kindred of the husband do not become united together by the fact of his taking a wife. Therefore they do not acquire any relationship of affinity.
On the contrary, Husband and wife are made one flesh. Therefore if the husband is related in the flesh to all his kindred, for the same reason his wife will be related to them all.
Further, this is proved by the authorities quoted in the text (Sent. iv, D, 41).
I answer that, A certain natural friendship is founded on natural fellowship. Now natural fellowship, according to the Philosopher (Ethic. viii, 12), arises in two ways; first, from carnal procreation; secondly, from connection with orderly carnal procreation, wherefore he says (Ethic. viii, 12) that the friendship of a husband towards his wife is natural. Consequently even as a person through being connected with another by carnal procreation is bound to him by a tie of natural friendship, so does one person become connected with another through carnal intercourse. But there is a difference in this, that one who is connected with another through carnal procreation, as a son with his father, shares in the same common stock and blood, so that a son is connected with his father's kindred by the same kind of tie as the father was, the tie, namely of consanguinity, albeit in a different degree on account of his being more distant from the stock: whereas one who is connected with another through carnal intercourse does not share in the same stock, but is as it were an extraneous addition thereto: whence arises another kind of tie known by the name of "affinity." This is expressed in the verse:
Marriage makes a new kind of connection,
While birth makes a new degree,
person
Reply to Objection 1. Although a cause is more potent than its effect, it does not always follow that the same name is applicable to the cause as to the effect, because sometimes that which is in the effect, is found in the cause not in the same but in a higher way; wherefore it is not applicable to both cause and effect under the same name or under the same aspect, as is the case with all equivocal effective causes. Thus, then, the union of husband and wife is stronger than the union of the wife with her husband's kindred, and yet it ought not to be named affinity, but matrimony which is a kind of unity; even as a man is identical with himself, but not with his kinsman.
Reply to Objection 2. Blood-relations are in a way separate, and in a way connected: and it happens in respect of their connection that a person who is connected with one of them is in some way connected with all of them. But on account of their separation and distance from one another it happens that a person who is connected with one of them in one way is connected with another in another way, either as to the kind of connection or as to the degree.
Reply to Objection 3. Further, a relation results sometimes from a movement in each extreme, for instance fatherhood and sonship, and a relation of this kind is really in both extremes. Sometimes it results from the movement of one only, and this happens in two ways. In one way when a relation results from the movement of one extreme without any movement previous or concomitant of the other extreme; as in the Creator and the creature, the sensible and the sense, knowledge and the knowable object: and then the relation is in one extreme really and in the other logically only. In another way when the relation results from the movement of one extreme without any concomitant movement, but not without a previous movement of the other; thus there results equality between two men by the increase of one, without the other either increasing or decreasing then, although previously he reached his actual quantity by some movement or change, so that this relation is founded really in both extremes. It is the same with consanguinity and affinity, because the relation of brotherhood which results in a grown child on the birth of a boy, is caused without any movement of the former's at the time, but by virtue of that previous movement of his wherein he was begotten; wherefore at the time it happens that there results in him the aforesaid relation through the movement of another. Likewise because this man descends through his own birth from the same stock as the husband, there results in him affinity with the latter's wife, without any new change in him.
Source: Summa Theologica (New Advent)