Weston joined Steve Albini and Todd Trainer in Shellac in 1991. Under Albini, Weston honed his studio production skills and has gone on to record and mix material for bands including Sebadoh, June of 44, Polvo, The Coctails, Archers of Loaf, Chavez, Rachel's, Ken Vandermark, 33.3 and Rodan. Weston was also Albini's Assistant Engineer on Nirvana's In Utero album. According to a 2006 interview, being a musician has helped shape Weston's work recording, mixing and mastering: "It’s obvious to me that the best recording engineers have played in bands. You understand the dynamic better and can almost become an unofficial band member during the session. And it’s pretty easy to tell on what sort of session your musical opinion is wanted or not." However, Weston's recording and mixing work is not limited to music: he occasionally freelances for National Public Radio, often working on comedy quiz show Wait, Wait, Don't Tell Me, which is headquartered in Chicago.