Fat was a nutritional substance.
Karna was the director of a company who were looking to create "the Beautiful People", people who were healthy, fit and very thin. She did this by using machines to drain the fat from people's bodies. (AUDIO: The Beautiful People)
The Adipose were composed entirely of fat. They could reproduce through parthenogenesis from the bodies of other beings. This meant they could be used to quickly reduce the weight of obese people. (TV: Partners in Crime)
One of the Anglican Marines of the Church stationed at Demon's Run was known as "The Fat One". He was initiated into the Headless Monks as part of Madame Kovarian's bargain with them for help keeping Amy and Melody Pond captive for the trap set for the Eleventh Doctor. (TV: A Good Man Goes to War)