Plato speaks to this in a story about Mankind. In the story, humans originally had two heads, four arms and four legs. Some humans were solely male, some were solely female and some were both. These humans had no need for marriage as they were complete in themselves. It was the Gods who separated the proto-men into halves, and now people have the need for marriage – finding their “other half” and reuniting the whole person. This story does NOT differentiate between same-sex and opposite-sex unions because some of the proto-men were wholly of one sex or the other – and are looking for their other half just the same as opposite-sex couples are.
If this is the case, natural moral law would SUPPORT same-sex marriage as a social stabilizing institution. This is something that I find important….