It might depend on certain factors, like your age, current level of physical fitness and metabolism, how overweight you are, how long you've been overweight, etc.
For me, it went really fast, but I was very sick as well and then started walking a lot and cutting down on portions to cut down on calories.
So not sure if it just falls off for most people, but add some exercise and cut calories (of course you're probably cutting a lot already with the alcohol), and you will probably start losing weight more quickly. Alcohol also lowers your metabolism, so that's another factor.