 At the 2010 census Weldon had a population of 2,642.The population density was 98.6 people per square mile (38.1/km²).The racial makeup of Weldon was 2,375 (89.9%) White, 5 (0.2%) African American, 82 (3.1%) Native American, 11 (0.4%) Asian, 1 (0.0%) Pacific Islander, 53 (2.0%) from other races, and 115 (4.4%) from two or more races.