I'll quote Robert Foster's The Complete Guide to Middle-earth:
During Lotho and Saruman's control of the Shire, Fredegar led a band of rebels in the Brockenbores [in the Eastfarthing near the hills of Scary], but he was captured and imprisoned in the Lockholes.
Fredegar was called Fatty before he was imprisoned and half-starved. He was a typical Hobbit in that, despite his friendship with Frodo, He had no desire to leave the Shire with him in 3018 to seek adventure, but became a partisan when it was necessary.
Fredegar also had a younger sister, Estella Bolger, who eventually was married to Meriadoc Brandybuck.
He just lived a normal Hobbit life after the Shire was freed from Sharkey's Men. It's quite possible that he became known as Fatty once again after he was able to eat his six daily meals once again.