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.
As a general guideline:
- Try not to run a huge deficit every day. For every two days that you run a massive deficit (+1000kcal less than your energy needs), you need one day with a significant caloric surplus (+1000kcal more than your energy needs) to balance it out.
- If want to run a moderate consistent deficit (i.e. 500-1000kcal per day), figure out how many calories you expend and take in daily with tracking tools like fitbit or myfitnesspal. Be precise!
- Eat lots of protein, veggies, and fruit. Don't cut out carbs or fat, just be mindful of their consumption.
- Try to take up some kind of training modality other than biking (you can still keep biking though). Unless you just absolutely adore biking, maybe consider trying out something new like resistance training or calisthenics. Hell, even running and swimming would be good additive.