The Church does, but it also operates under the auspices of the state.
Marriage serves a secular function as well, and I don't just mean paying different tax rates.
Children born in marriage are better achievers in all types of socially-desireable ways, from attending college to avoiding drug abuse. Likewise marriage settles in law paternity of chidren and provides social boundaries (you don't mess with someone's wife) which promotes social order.
So it is religious, but there is also a secular social interest in marriage.
SD
most of those social benefits come from adhering to beliefs promoted by the church.