Like most Starfleet officers, Zweller attended Starfleet Academy, graduating in 2327. As an ensign, Zweller's first assignment was the USS Ajax, due to begin a deep space mission under the command of Captain Narth.
Prior to his arrival on the Ajax, Zweller spent several days at Starbase Earhart along with his friends, Jean-Luc Picard and Marta Batanides. During his stay there, he spent a lot of time socializing and playing dom-jot at the Bonestell Recreation Facility. On one such occasion, Zweller was challenged to a game by a group of Nausicaans, a game in which they won, much to his displeasure.
Believing the Nausicaans had cheated by using some sort of magnetic device, Zweller returned to the bar late one night and rigged the table himself, before challenging the Nausicaans to a rematch. He won the game, but it didn't take the Nausicaans long to determine that he, too, had cheated. After a brief exchange of words, a bar fight broke out in which Batanides was knocked unconscious and Picard stabbed through the heart, requiring him to undergo surgery.
Cortan Zweller was played by actor Ned Vaughn in his only Star Trek appearance. The spelling of his first name comes from the script,  and is also used in the Star Trek: The Next Generation Companion (2nd ed., p. 235). The spelling "Cortin" is used in the Star Trek Encyclopedia (2nd ed., p. 576) and various novels.
The script describes Zweller as "a tall, lanky, twenty-one year old, with long hair that probably barely passes regulations." This would put his birth around 2306.
The Pocket TNG novel Rogue reveals Commander Zweller's affiliation with Section 31, which ended his career in disgrace after a S31 operation resulted in the loss of his assigned starship, the USS Slayton (β).