 Born in Croy, a village between Inverness and Nairn in Scotland, Weldon started his footballing career with Kilsyth Rangers based in Kilsyth, North Lanarkshire before signing for Airdrieonians on 27 May 1924 for a transfer fee of £5.With Airdrieonians, such were his performances that he found himself picked for the first team ahead of Scottish international players, Willie Russell and Hughie Gallacher.He was part of the side that finished second in Division One two years running, in 1924–25 (four appearances) and 1925–26 (19 appearances and four goals), and scored 26 goals in 26 appearances as the club finished fourth in 1926–27.