Is it possible to lose enough weight for a fatty liver to go back to normal?

Depends. Fatty liver has been linked to obesity, however it is typically seen in people who place alot of stress on the liver's function. Typically seen in alcoholics, however when seen in non-alcoholics it is called non-alcoholic steatohepatitis (nash). Weight loss needs to be achieved to make a change, especially will help those associated with obesity.
Yes. Yes it is possible. I recommend you watch a documentary called 'super size me". The guy in it basically develops fatty liver while eating a certain way and once he goes back to a healthy diet his liver returns to normal.