The son of Dorothy and Frederick Weller. Weller had a "middle-class Catholic" upbringing. As a result of his father's army work, Weller spent many years abroad during his childhood. His family lived in Germany for several years before eventually moving to Texas, where he attended Alamo Heights High School in San Antonio. While enrolled at North Texas State University, he played trumpet in one of the campus bands. He graduated with a Bachelor of Arts in Theatre, and began his acting career after graduating from the American Academy of Dramatic Arts.
Weller's stage career began in the 1970s with appearances on Broadway in Full Circle. He has appeared in more than 50 films and television series. n 1995, he appeared in Screamers, a science-fiction film based on the short story "Second Variety" by Philip K. Dick. On television, he played the shuttle captain in the short-lived show Odyssey 5. Weller has also directed various projects for television.
On January 15, 2010 Weller was seen in a teaser trailer for the companion documentary God of War: Unearthing the Legend that will be featured in the upcoming game God of War III and that Weller will host.
Weller is a fan of Italian filmmaker Michelangelo Antonioni. In 2004, Weller completed a Master's degree in Roman and Renaissance Art at Syracuse University and occasionally teaches courses in ancient history at the university.