Prohibited and Unprohibited Relationships Due to Holy Baptism

From the opening paragraph to the section entitled “Concise and Accurate Instructions Concerning Marriages”: Since the sacred Canons, Apostolic, Conciliar, and Patristic, in speaking in various parts about lawful and unlawful marriages (e.g., Ap. c. XIX; cc. III and LIV of the 6th; c. II of Neocaesarea; cc. XXIII, XXVII, XXVIII, LXVIII, LXXVI, LXXVII, LXXVIII of Basil; c. XI of Tim.; and cc. V, XIII or Theophilus), requires a knowledge of marriages to be combined with them, therefore and on this account we have judged it reasonable, after interpreting the sacred Canons, to insert in a special place within the volume, for a clearer comprehension on the part of the more unlearned, a concise and at the same time accurate set of instructions regarding marriages allowed by the laws as well as those prohibited, in view of the fact that such instructions are needed by all, persons in general, but especially by the holy Prelates and Spiritual Fathers and Priests, who have an obligation to examine into all these matters....
This relationship results when one sponsors a child at the ceremony of Holy Baptism. For the man who undertakes this sponsorship is making the child in question his spiritual son or daughter, as the case may be; accordingly, he in fact becomes a closer and more intimate relative and father of the child than is its carnal father, because just as much as the spirit is higher than the body the relationship of the spirit is higher than that of the flesh. Hence in accordance with this ratio of intimacy c. LIII of the 6th Ecumenical Council asserts that relationship in respect of spirituality is greater than any relationship in respect of carnality. Some persons, however, in reading the present Canon failed to understand it in this vein, as respecting the quality of intimacy, but took it to refer to quantity of degrees. Wherefore they even extended the relationship due to baptism to the seventh degree. Others, again, even prohibited the eighth degree, which is more than holds with respect to blood relationship. Though this may not please most men, as Blastaris says (alphabetical section Beta), yet it pleases them to have only those persons prohibited who are prohibited by the law. But the law prohibited, not collateral relatives—brothers and sisters, that is to say, of a godfather and of a godson, but only those in the direct line; and even these not to the eighth degree, but only to the third. In other words, the law simply prohibited a godfather from marrying his goddaughter, or her mother or her daughter, but neither may the son of the godfather take to wife any one of these three. So:
Prohibited Marriages
1.—A godfather (or his carnal son) may not marry his goddaughter, i.e., any girl that he has baptized; because she is a spiritual daughter of his and of the first degree in relation to him, while in relation to his son she is a spiritual sister, and consequently of the second degree.
2.—Nor her mother, nor her daughter; because they are of the second degree. 
3.—None of the godfather’s children may marry the mother of their father’s godchild, since they are considered nephews and nieces in relation to her, and are of the third degree. 
4.—Nor may any child marry a daughter of his father’s goddaughter (or conversely), because he is considered a spiritual uncle in relation to her, and consequently is of the third degree.
Unprohibited Marriages
1.—A son of the godfather may marry the sister of her godfather’s son, according to Blastaris, or vice versa, the brother of a godfather’s godson may marry the godsister of his brother.
2.—The carnal son of a godfather may marry the carnal sister of the godson; for according to most authorities she is of no degree, owing to her relationship being collateral.
3.—Likewise the brother of a godfather may marry the sister of his godson; and conversely the brother of the godson may marry the sister of the godfather.
4.—Two spiritual brothers or spiritual sisters, or a spiritual brother and a spiritual sister, having the same godfather, may marry two carnal sisters.
Prohibited Marriages
1.—If perchance two children, one male and the other female, happen to be baptized by one and the same godfather, they may not marry each other, because they are spiritually brother and sister, according to most holy St. Sisinnius, and are of the second degree.  
2.—A man may not marry the widow of his spiritual brother, because he too is considered to be a brother of hers, owing to his brother’s having contracted a relationship with her making the two of them one flesh, and therefore she is of the second degree in relation to him.
3.—Likewise if the husband baptizes one child, and his wife another, these children may not intermarry; because it is plain that they were baptized by the same sponsor, owing to the fact that a married couple is accounted one flesh, notwithstanding that the godfather and the godmother are not one and the same person.
4.—Likewise a son-in-law may not marry the goddaughter of his fatherin- law, since she is considered a sister of his dead wife. One and the same man can never marry two carnal or spiritual sisters.
Unprohibited or Doubtful Marriages
1. But if the father-in-law baptize one child, and the son-in-law another, these children may intermarry, because a father-in-law is related to his son-in-law collaterally (a latere), as some say. Yet a father-in-law in relation to his son-in-law is considered to be related to him lineally and not collaterally, owing to the fact that his son-in-law is united with his daughter into one flesh. Hence such a marriage is doubtful and worth discussing.

Note, moreover, that if any man stands sponsor for his own child, he is to be separated from his wife, because they have become spiritual brothers of hers, according to what Blastaris says (alphabetical section Beta). Likewise note that sponsors must be Orthodox Christians, and not infidels or heretics, according to Symeon of Thessalonica (ch. 280). That is why Balsamon (Reply 32) vehemently forbids Latins, or Armenians, or Nestorians, and other such persons to become sponsors for Orthodox children, and insists that those who allow such a thing ought to be excluded from communion, on the ground that they are guilty of having entered into communion with heretics.1 In writing about sponsors to a certain monk named Dionysius, Elias the Metropolitan of Crete says that “if sponsors knew exactly what Dionysius the Areopagite specifies as qualifications for sponsors, and what care and caution they ought to exercise in regard to their godchild (for Dionysius the Areopagite, in ch. 7 of his treatise concerning the Ecclesiastical Hierarchy) asserts that when the godfather at a baptism says, “I renounce Satan, and join the ranks of Christ,” he is declaring this: “I acknowledge and vow that I will persuade this child, by the teaching and good education I am to give it, to renounce the Devi1 and his works of its own accord and by itself when it comes into possession of mature reason, and to join the ranks of Christ, and to vow these divine vows; if, I say, they actually knew this, they would have grave scruples about standing sponsor at baptisms, even though they were fervidly invited to do so. Since, however, they do not know this, I say, and since a custom has prevailed of letting women too stand sponsor at baptisms, there is nothing to prevent a man from standing sponsor for a child at baptism when that child is the first one of a certain person to be baptized, and afterwards, in the absence of the man, there is nothing to prevent his wife from standing sponsor likewise for a second child of the same person” (p. 340 of Jus Graeco- Romanum). Nevertheless, these children cannot intermarry, as we have said before. But it is only the one who stands sponsor for a person’s child that is called a syntecnus, and not also his brothers, according to Peter the Chartophylax (p. 369, ibid.). See also the Footnote to c. VI of Caesarea.

Source: http://orthodoxinfo.com/praxis/relationship_due_to_baptism.aspx