Police have not identified a motive for the shooting.
Caffall's mother, Linda Weaver, released a statement Monday expressing sorrow for the victims and saying her son was ill, but didn't elaborate.
Richard Weaver told KPRC that he and his wife had not spoken to Caffall for several months.
Caffall, who was divorced, quit his job about nine months ago and swore he would never work for anyone again, Weaver told the station.
"We were hoping he'd kill himself before doing something like this," Richard Weaver said. "We are just devastated for the families this SOB killed."
Caffall was a devoted gun enthusiast who posted several photos of modern and antique rifles to his Facebook page.
On June 7, he posted a photo of a Czech vz. 58 assault rifle and two banana clips, along with a message that he couldn't "wait to try it out on the range."
Another photo showed a Russian Mosin-Nagant rifle and two canisters of ammunition.
"I just got a new toy!" Caffall wrote.
The page also contained several quotations that referenced war, conflict and violence.
One inaccurately attributed to writer George Orwell said, "People sleep peaceably in their beds at night only because rough men stand ready to do violence on their behalf."
In a statement posted on the school's website, Texas A&M President R. Bowen Loftin said the shooting marked “a sad day in the Bryan-College Station community.”
“My thoughts and prayers, as well I am sure of the entire Aggie community, go out to the families and close friends of those who died so tragically, those who were injured and anyone else personally impacted by this senseless act of violence," Loftin said.
-- By Philip Caulfield/New York Daily News
With Chris George In College Station, Texas, and Corky Siemaszko and Bill Hutchinson in New York