DUDE! If you are burning 1,200 to 1,600 calories JUST on a bike alone and only eating 2,000 calories you are severely undereating, and this is just plain bad for you regardless of if you want to lose weight or not. You're doing more longterm damage than anything.
Just put it this way, if you burn 1,200-1,600 calories in a workout, you burn about another 1,500-2,400 (depending on bodyweight and metabolism, I'm guessing you will be at the higher range if you're a big guy trying to lose weight) just by being alive and living a normal life. You're expending 2,700 to 4,000 calories a day and only eating 2000? That's as much as a 2000 calorie deficit every day! You can't expect anything but negative results with that kind of deficit.