CINCINNATI — Jim Obergefell says he “instantly pictured growing old” with John Arthur when they fell in love here in 1992. Just seven weeks after they began dating, Mr. Arthur gave Mr. Obergefell a ring set with diamonds — a sign that, in their hearts if not in law, they were married.

Two decades later, with Mr. Arthur dying of amyotrophic lateral sclerosis (Lou Gehrig’s disease), they did marry, aboard a medical charter jet on the tarmac of an airport in Maryland — a state where, unlike Ohio, gay people could wed. When Mr. Arthur, 48, died in October 2013, Ohio refused to list Mr. Obergefell as his spouse on the death certificate. Furious, Mr. Obergefell sued.

Now Mr. Obergefell, 48, a soft-spoken, bespectacled real estate agent who says he never intended life as an activist, is the lead plaintiff in a Supreme Court case that could topple Ohio’s ban and establish a national right to same-sex marriage. As the court prepares to hear arguments Tuesday, gay rights advocates around the country point to his case as evidence of discrimination.

But here in Cincinnati, where Mayor John Cranley calls Mr. Obergefell a “historic figure,” his case has become the measure of something else entirely: how far the gay rights movement has come in one of the most traditionally conservative corners of the Midwest.