Wesson is the son of Keith Wesson, who played at Ohio State from 1983 to 1987. Kaleb attended Westerville South High School and played alongside older brother Andre. Kaleb became a starter as a sophomore on the state runner-up team. He had seven points and four rebounds as the Wildcats beat Lima Senior High School 57–55 to claim the state title. Wesson scored a school-record 49 points in a 68–67 loss to Upper Arlington High School on January 24, 2017. As a senior, Wesson averaged 22.4 points and 10.9 rebounds per game and shot 67 percent from the floor on a team that finished 19–6. He was named Ohio Mr. Basketball.
Recruiting
Wesson was a four-star recruit, rated as the No. 75 overall player and No. 6 center in his class, and committed to Ohio State.
College career
After arriving at Ohio State, Wesson worked to get in better shape, losing weight by cutting out soda and juice. He averaged 10.2 points and 4.9 rebounds per game on 56 percent shooting as a freshman. He was named to the Big Ten All-Freshman team. Wesson had a career-high 31 points in a 75–56 win against Youngstown State on December 18, 2018. On March 1, 2019, Wesson was suspended for violating athletic department policy. He missed three games and returned in time for a Big Ten Tournament matchup with Indiana, finishing with 17 points, 13 rebounds, three assists, three blocks and two steals in the 79–75 victory. Wesson was an All-Big Ten honorable mention selection. As a sophomore, Wesson averaged 14.6 points, 6.9 rebounds and 1.8 assists per game, shooting 50 percent from the floor and 34 percent from three-point range. After the season, he declared for the 2019 NBA draft but ultimately opted to return to Ohio State. Wesson worked on his conditioning coming into his junior year by boxing with strength and conditioning coach Quadrian Banks. He was ranked the sixth best player in college basketball by ESPN in October 2019. After scoring 10 points and grabbing 11 rebounds in a 76–51 victory over Villanova, Wesson was named Big Ten player of the week on November 18. He had 28 points and 10 rebounds in a 106–74 rout of Penn State, helping the Buckeyes notch 100 points against a Big Ten rival for the first time since 1991. At the close of the regular season, Wesson was named to the Second Team All-Big Ten by the coaches and media. As a junior, Wesson averaged 14.0 points and 9.3 rebounds per game, shooting 42.5% from beyond the arc. Following the season, he declared for the 2020 NBA draft.