Weller studied under George Bellows at the Chicago Art Institute and also at the British Academy in Rome. He instructed at the Denver Art Academy during the 1920s. He left Denver for a time during the 1940s and worked in New Orleans and Southern California.

He executed murals at the Colorado State Capitol Annex as well as East High School in Denver. He also painted scenery for the Denham Theater and Elitch Gardens in Denver. In addition to actively working in Denver, he also established a studio in Grand Lake, Colorado.