In 2015, as a freshman at Kansas, Weiman appeared in 21 games (seven starts), going 2–7 with a 6.75 ERA.[4] As a sophomore in 2016, he became a full-time starter, appearing in 17 games in which he went 2–7 with a 6.82 ERA.[5] In 2017, in Weiman's junior season, he moved to the bullpen where he greatly improved, pitching to a 5–1 record with a 2.80 ERA, striking out 55 batters in 45 relief innings pitched. After his junior year, he was drafted by the Pittsburgh Pirates in the eighth round of the 2017 Major League Baseball draft.[6][7]
Weiman did not play a minor league game in 2020 since the season was cancelled due to the COVID-19 pandemic.[16] For the 2021 season, he returned to Indianapolis.[17] He missed playing time in August due to injury.[18] Over 35 relief appearances, Weiman went 5–0 with a 4.76 ERA and 45 strikeouts over 45+1⁄3 innings.[19] He returned to the Indians to begin the 2022 season.[20] On June 27, 2022, he was released.[21]
Seattle Mariners
On July 6, 2022, the Seattle Mariners signed Weiman to a minor league contract and assigned him to the Double-A Arkansas Travelers.[22] Over 33 relief appearances between the Indians and Travelers, he went 3-1 with a 4.47 ERA, 42 strikeouts, and six walks over 44+1⁄3 innings.[23] Weiman elected free agency following the season on November 10.[24]
On December 5, 2022, Weiman re-signed with the Mariners on a minor league contract. Weiman spent the 2023 season with the Triple–A Tacoma Rainiers, making 44 appearances out of the bullpen and recording a 5.17 ERA with 53 strikeouts across 54 innings of work. Weiman elected free agency following the season on November 6.[25]
Chicago Cubs
On February 2, 2024, Weiman signed a minor league contract with the Chicago Cubs.[26] He spent the season with the Double-A Tennessee Smokies, also making one appearance for the Triple-A Iowa Cubs. In 42 appearances out of the bullpen for Tennessee, Weiman compiled a 4-0 record and 2.77 ERA with 52 strikeouts and 7 saves across 48+2⁄3 innings pitched. He elected free agency following the season on November 4.[27]
Houston Astros
On January 6, 2025, Weiman signed a minor league contract with the Houston Astros.[28] He made 26 appearances for the Triple-A Sugar Land Space Cowboys, struggling to a 7.94 ERA and 2-1 record with 28 strikeouts across 28+1⁄3 innings pitched. Weiman was released by the Astros organization on August 4.[29]
Los Angeles Angels
On February 23, 2026, Weiman signed a minor league contract with the Los Angeles Angels.[30]