A clinic or resort where people go to lose weight. This is a somewhat derisive term for such an establishment.
She spends all her vacations at a fat farm but it hasn't helped so far.
Laverne and Shirley went to the fat farm.
The future solution to a growing epidemic in the United States in which all obese people will be shipped off in secured freight trains, prodded and herded onto large farm establishments. Once at the farm, the fatties will undergo a harvesting method where large industrial strength lipo suction machines will suck the lard out of each carcass which would then be refined into fuel. This fuel will provide enough energy to power an entire state for decades providing a reliable source for alternative fuel. Better yet, no one will have to deal with fat people ever again.
Uh Oh, Betty's packing the pounds on, if she keeps it up we'll send her off to the fat farm.