Sawyer and his twin brother Sullivan were just a year old when they were hired on the popular CBS sitcom. They starred alongside their real-life sister Madylin, who was five.
"I play with them a lot and tickle them," Madylin told ET in 1996. "I like them so much."
Following the tragedy, Madylin took to Facebook to "encourage everyone to reach out to the ones you love."
In 2005, Sawyer told us he was sad that the show was ending and Madylin shared her early memories on the show.
"My first memory is when they had to dress up as me," Madylin said. "They had to dress up as little me and they put little pigtails in. I remember that because they punch me every time I mention it."
Sawyer was visiting family in Texas on Thursday when he allegedly shot himself on the front porch of the family home. He was 19.
Sawyer's TV parents Ray Romano and Patricia Heaton commented on the devastating loss, issuing statements expressing their condolences.
"I'm shocked, and terribly saddened, by the news about Sawyer," Romano said. "He was a wonderful and sweet kid to be around."
"He is gone from us far too soon," Heaton said. "The loss the Sweeten family is experiencing is unimaginable."