In 1992, the family lost six-week-old Kenneth after he died from complications caused by his premature birth.
Durham Police said Colin went swimming with two friends, also 16, to cool off in the warm weather. The teenagers were in a section of the river known locally as The Batts when Colin began to struggle and was unable to reach the river bank. His friends raised the alarm at around 5.15pm on Saturday when Colin failed to emerge from the water.
A joint operation involving police, ambulance, the fire service, the RAF and search and rescue teams was launched and continued throughout the night.
The force spokeswoman said a police underwater search team found Colin's body at around 4.20am on Sunday.
The death was not being treated as suspicious, the spokeswoman said, describing it as "a tragic accident". Colin's family were said to be "distraught".