He was then drafted by the Cincinnati Reds in the sixth round of the 2013 MLB Draft. Weiss signed with the Reds and made his professional debut with the Arizona League Reds, and also played for the Billings Mustangs that year. Weiss spent 2014 with the Dayton Dragons of the Class AMidwest League, for whom he was 2-4 with a 2.42 ERA, with 80 strikeouts in 63.1 innings. Weiss spent 2015 with the Daytona Tortugas of the Class A-Advanced Florida State League and the Pensacola Blue Wahoos of the Class AA Southern League. He had a Pensacola-record 25 saves, and 30 saves in total between the two teams. In 63 2/3 innings, he had a 1.98 ERA and gave up 42 hits and 15 walks, while striking out 90 batters. He was a 2015 Southern League All Star, and a 2015 MILB.com Cincinnati Organization All Star. After the season, he played in the Arizona Fall League. He suffered an elbow injury in early 2016 while in major league spring training, did not pitch that year, and underwent surgery to transpose the ulnar nerve and to remove scar tissue in his pitching elbow in December 2016. In 2017, Weiss was 2-1 with one save and a 2.08 ERA, and 19 strikeouts in 13 innings, for Daytona, and 2-4 with nine saves and a 2.89 ERA, and 37 strikeouts in 28 innings, for Pensacola. Between the two teams, he averaged 12.3 strikeouts per nine innings. The Reds added him to their 40-man roster after the 2017 season. In 2018 in the minors, between the Arizona Reds, Pensacola Blue Wahoos, and the Louisville Bats he was 3-3 with one save and a 5.40 ERA, and 26 strikeouts in 24.1 innings. Reds manager Bryan Price said in spring training in 2018: "if he doesn't make the team I imagine we'll see him at some point during the year." The Cincinnati Reds added Weiss to their active roster on their Opening Day, March 30, 2018, and he made his major league debut on April 12, at Great American Ball Park against the St. Louis Cardinals. Weiss was released by the Reds on September 1, 2018.
On November 1, 2018, Weiss signed a minor league deal with the Minnesota Twins. He was released by the organization on July 15, 2019. In 2019, pitching for the Class AA and Class AAA affiliates of the Minnesota Twins, he was a combined 1-3 with a 7.24 ERA in 16 relief appearances, with 30 strikeouts in 27.1 innings.
On July 19, 2019, Weiss signed with the Long Island Ducks of the Atlantic League of Professional Baseball. Pitching for them in 2019 he was 4-1 with one save and a 4.68 ERA in 16 relief appearances, as he struck out 34 batters in 25 innings. He became a free agent following the season.
On February 18, 2020, Weiss signed a minor league deal with the Cleveland Indians. Weiss was released by the Indians on May 29, 2020.
Team Israel
He pitched for Team Israel at the 2019 European Baseball Championship, going 1-0 with one save and a 0.00 ERA as in four relief appearances he pitched 6.1 innings and gave up one hit and three walks while striking out five batters. He also pitched for the team at the Africa/Europe 2020 Olympic Qualification tournament in Italy in September 2019, which Israel won to qualify to play baseball at the 2020 Summer Olympics in Tokyo. In the tournament he was 0-0 with a 6.00 ERA over 3.0 innings in which he gave up one hit, four walks, and had six strikeouts.