Welge made his World Championship debut in the 2002 BDO World Darts Championship where he lost in the first round 3–2 to Eric Clarys. He made his PDC debut in the 2006 PDC World Darts Championship, where he was defeated 3–0 by Alan Warriner-Little in the first round. Four years later, he qualified for the 2010 PDC World Darts Championship, but was beaten 3–0 by Mark Dudbridge in the first round. In the 2011 PDC World Darts Championship he was close to beating Colin Lloyd in the first round, having three matchdarts, but ultimately lost 3–2.