Hellweg attended St. Dominic High School in O'Fallon, Missouri, and Florida State College at Jacksonville.

The Angels traded Hellweg, Jean Segura, and Ariel Peña to the Milwaukee Brewers for Zack Greinke on July 27, 2012.

[6] In 10 games (6 starts) split between the Double–A San Antonio Missions and Triple–A El Paso Chihuahuas, he struggled to a 10.95 ERA with 17 strikeouts across 24+2⁄3 innings pitched.

In 2018, Hellweg made 24 appearances for the Triple–A Indianapolis Indians, compiling a 1.33 ERA with 25 strikeouts and 11 saves across 27 innings of work.

[10] On June 26, 2018, Hellweg signed with the Hiroshima Toyo Carp of the Nippon Professional Baseball (NPB).

[14] On February 22, 2021, Hellweg signed with the Long Island Ducks of the Atlantic League of Professional Baseball.