Cutter died May 21 in the New Mexico city after a long battle with stomach cancer, said organizers of the Albuquerque International Balloon Fiesta, now held every October.
A former Air Force pilot, Cutter had not been schooled in ballooning when he accidentally went aloft in 1971 when a crew member released a tether. Fortunately, he was a "fast learner," according to the Iowa-based National Balloon Museum.
"I got hooked on balloons right off the bat," Cutter told The Times in 1985.
To help an Albuquerque radio station mark its 50th anniversary in 1972, Cutter held a hot-air balloon rally and race that began in a shopping mall parking lot. The 13 competitors drew an unexpectedly large crowd of about 10,000, the Associated Press reported in 1997.
The event marked the beginning of the annual International Balloon Fiesta.
Last year's nine-day festivities drew about 500 balloonists and an estimated 810,000 spectators, according to organizers.
"As the founder of the Balloon Fiesta, he put Albuquerque on the map for many around the world," Albuquerque Mayor Richard J. Berry said in a statement.
Cutter also produced the first World Hot Air Balloon Championship in 1973 and held it in Albuquerque. More than 130 balloon crews from 14 countries participated in the event, which helped establish the city as a "mecca of ballooning," the museum said.
Sidney Dillon Cutter was born May 9, 1934, in Albuquerque to William P. Cutter and Virginia Dillon Cutter, who founded Cutter Flying Service in 1928. His grandfather, Richard C. Dillon, was New Mexico's governor from 1927 to 1931.
As a child, Cutter learned to fly while sitting on his father's lap and legally soloed for the first time at 16.
He spent two years at the University of New Mexico and a semester at the University of Alaska at Fairbanks.
In 1955, he joined the Air Force and flew cargo around the world until 1960, when he rejoined his family's aviation business. For more than a decade, he served as the company's president.
After buying his first balloon in 1971 in honor of his mother's 62nd birthday, he increasingly turned toward the pursuit.
He formed one of the world's largest balloon clubs and founded the World Balloon Co., which taught piloting and performed at promotional events.
The company also built two of the world's largest thermal airships, according to the balloon museum.
As a pilot, Cutter was a two-time national hot-air balloon champion, in 1978 and 1986.
While trying to explain the appeal of an antique form of aviation, Cutter once told The Times: "It's like floating through the air on a magic carpet ride."
He is survived by Jewel, his wife of 31 years; a daughter, Sheryl; a brother, Bill; and six grandchildren.