He signed for the Dons in 1984 and made his debut on New Years Day 1985 against Oldham Athletic. Early in his career at the club he had loan spells at Porin Pallotoverit and Koparit in Finland before establishing himself as a regular in the Wimbledon side. He went on to make 138 league appearances for the club, scoring 26 goals as they established themselves as a First Division club and being founders members of the new FA Premier League in 1992. His best season was the 1986–87 campaign, where he played 23 times in the league and scored eight goals in their first campaign as a First Division club, finishing an impressive sixth and actually leading the table in early September. The highlight of Wimbledon's remarkable success story came at the end of the 1987–88 when they reached the FA Cup final and achieved a shock 1–0 win over Liverpool. However, a broken leg meant that Fairweather was not in the squad for that game, although he did appear 21 times in the league prior to his injury and scored four goals to help achieve a seventh-place finish. By the end of his time at Wimbledon, he had become the club's "forgotten man", failing to make a single league appearance in his final season and played just 11 times collectively in the two seasons before that.