Combine ketchup, mayonnaise, and 1/4 teaspoon pepper in a small bowl.
Place sugar, salt, remaining 1/2 teaspoon pepper, beef, and garlic in a bowl; gently combine. Divide into 16 (3/4-ounce) balls; lightly coat with cooking spray.
Heat a large cast-iron skillet over high. Coat pan with cooking spray. Add 4 beef balls to pan; use a large offset spatula to press each portion into a 2-inch-wide patty. Cook until well browned, about 1 minute. Turn patties; top each with 1 1/2 teaspoons cheese. Cover pan; cook 30 seconds or until cheese melts. Remove patties from pan; arrange in stacks of 2. Repeat procedure with remaining beef balls and cheese.
Top each bottom bun with 1 1/2 teaspoons ketchup mix, 2 patties, 1 tomato slice, 2 onion slices, and 1 lettuce leaf. Cover with bun tops.