Well … I suppose that one could say that from the moment that the Roman state began to support the Church in various ways, it was in some sense supporting marriage. In English/British North America, several colonies had state churches from the earliest times. Those churches generally claimed an exclusive right to marry people and insisted that people be married, although some portion of the population either lived outside the area in which limited supplies of ministers exercised their authority or flouted their authority in their actual communities.
A good book on the subject of legal regulation of sex in colonial North America is Goodbeer’s SEXUAL REVOLUTION IN EARLY AMERICA, which I’ve assigned to my students in the fall. It deals not only with marriage, but with other aspects of sex law: laws about sodomy, incest, polygamy, bestiality, etc.