Curtis, 58, died in his sleep sometime after going to bed Thursday night. The news shocked and saddened his colleagues.
Councilwoman Joyce Brown said she was told of the death early Friday. Brown said she last saw Curtis at a holiday lighting ceremony Monday night at Commons Park and he seemed fine.
"He was very much loved by the citizens," Brown said. "The city staff and employees had great respect and love for him. He loved his community."
State Sen. Jerry Stevenson, a longtime friend and former Layton mayor, said Curtis was willing to do anything for the city and was very involved in community matters. He also was a military booster, the senator said.
"I think Hill Air Force Base lost a great friend in Steve," Stevenson said. "Steve was totally supportive of the Air Force and what they do for us."
Curtis was first elected mayor in 2005 after serving a decade on the Layton City Council and was completing his second term. He did not run for another term in the November election, telling The Salt Lake Tribune he wanted to spend more time with his family.
Bob Stevenson was elected and will take over the mayor's office in January. Until then, Councilman Jory Francis, the mayor pro tem, will handle the mayoral duties.
Curtis who was born in Salt Lake City and raised primarily in Ogden and his wife, Rae Lynn, had five children. He was a telecommunications worker for years.
In addition to serving as mayor of Davis County's largest city (population 68,677), Curtis had seats on the executive board of the Economic Development Corp. of Utah and the Wasatch Integrated Waste Management District board of directors.
The late mayor, who earned about $21,800 a year plus benefits in his part-time public office, ran into financial difficulties after being laid off as a banking manager and filed for bankruptcy in 2010. He was undeterred by the setback. Brown said he continued to work hard.
"Through all of his struggles, he's been there taking care of his duties for the city," she said. "He put that ahead of his own struggles and concerns."
City Manager Alex Jensen also said Curtis never let the economic challenges get him down and continued to be upbeat. The mayor made city employees feel valued, he said.
"He enjoyed being mayor not because of the accolades he got but because he was able to do good," Jensen said. "He was a very good mayor and a blessing to the community."