It certainly could be alcohol and I'd say with your level of consumption that's most likely. The other things worth checking, particularly given your high BMI, are your cholesterol and triglyceride levels. There is a condition called 'non-alcoholic steatohepatitis' which occurs more often in fat people and obviously in those with high fat levels in the blood. For whatever reason the fat induces an inflammatory reaction in the liver. Worth checking, but like I and others say it's probably all just down to the booze.
Clearly, too, your physician should be checking hepatitis serology and all the other blood tests you do when someone has raised LFTs.
QDM