From Between Two Worlds:
Last week Robert P. George, Ryan T. Anderson, and Sherif Girgis posted online a lengthy, detailed natural-law answer to the question “What Is Marriage?” to be published in theHarvard Law Review. It sets forth the best arguments and seeks to answer the best objections related to the nature of marriage.
Writing at Slate, NYU Law Professor Kenji Yoshino, a prominent gay-rights legal scholar, offered a response, “The Best Argument Against Gay Marriage.”
George, Anderson, and Girgis respond today: “The Argument Against Gay Marriage: And Why It Doesn’t Fail.”
In their response, they restate some of their argumentation:
Our article offers detailed responses to the most significant objections to our view: that it  has no principled grounds for recognizing infertile couples’ marriages,  ignores the needs of same-sex attracted people,  is morally similar to support for anti-miscegenation laws,  assumes the mutability of sexual desire,  relies on religious belief, or [6[ fails to show the concrete harm in redefining civil marriage.
We also show that those who would redefine civil marriage, to eliminate sexual complementarity as an essential element, can give no principled account of why marriage should be (1) a sexual partnership as opposed to a partnership distinguished by exclusivity with respect to other activities (including non-sexual relationships, as between cohabiting adult brothers); or (2) an exclusive union of only two persons (rather than three or more in a polyamorous arrangement). Nor can they give robust reasons for making marriage (3) a legally recognized and regulated relationship in the first place (since, after all, we don’t legally recognize or closely regulate most other forms of friendships).
The dialogue is detailed, but the arguments are relatively clear. The above will take you to the best arguments on both sides. And I think the conjugal view clear takes the day, even from a merely natural law perspective.