Wallis was the son of Hamilton Wallis, a prominent lawyer of East Orange, New Jersey. He had a brother, Nathan C. Wallis and a sister, Emeline Waldron Wallis, who married James Carr Dunn of London, England. Though Wallis was a lineman, he was a frequent ball carrier for Yale. In November 1892, an article reported that Wallis was running with the ball in his old form, getting off to a quick start, “hitting the line hard and tackling equally hard.”