Weatherspoon went to the Spurs in the second round (49th overall) of the 2019 NBA Draft, then proceeded to spend the majority of the season in the G League with the Austin Spurs, where he averaged 14.8 points, 5.2 assists, 3.8 rebounds and 1.1 steals per contest over 36 games (35 starts). He also drained 1.4 three-pointers per game on 33.6 percent shooting from behind the arc. Weatherspoon's best G League game came Jan. 3 during a win over Greensboro, when he produced 30 points, six rebounds, four assists, four three-pointers, two steals and two blocks over 33 minutes. He nearly double-doubled Feb. 27 at Aqua Caliente, tallying 19 points, eight rebounds, five assists and a steal. The 6-foot-3 guard scored 20 or more points in seven G League games. He made his NBA debut Feb. 8 against the Kings, then went on to appear in two more games before the NBA paused its season due to the coronavirus pandemic. Once the league resumed play in the Orlando bubble, Weatherspoon became a regular part of San Antonio's rotation, appearing in all eight seeding games. In the Spurs' first seeding game, Jul. 31 against Sacramento, Weatherspoon scored a season-high four points; he'd go on to match that Aug. 7 against Utah. The Mississippi State product made his first career three-pointer Aug. 3 against the Sixers.