A small minority of married couples are infertile. However, excluding sterile couples from marriage, in all but the most obvious cases such as those of blood relatives, would be costly. Few people who are sterile know it, and fertility tests are too expensive and burdensome to mandate. One might argue that the exclusion of blood relatives from marriage is only necessary to prevent the conception of genetically defective children, but blood relatives cannot marry even if they undergo sterilization. Some couples who marry plan not to have children, but without mind-reading technology, excluding them is impossible. Elderly couples can marry, but such cases are so rare that it is simply not worth the effort to restrict them. The marriage laws, therefore, ensure, albeit imperfectly, that the vast majority of couples who do get the benefits of marriage are those who bear children.
Homosexual relationships do nothing to serve the state interest of propagating society, so there is no reason for the state to grant them the costly benefits of marriage, unless they serve some other state interest. The burden of proof, therefore, is on the advocates of gay marriage to show what state interest these marriages serve.