I'm not real familiar with how or what fit bit tracks.
Go here www.freedieting.com/tools/calorie_calculat
and calculate your Basal Metabolic Rate (BMR) in the exercise drop down box. That's how many calories you would burn if you didn't get out of bed all day. AKA that's how many calories you burn just to stay alive.
Fit bit says your burning like 1600+ ON TOP of your BMR. That'd easily put you at like probably 2600+ to maintain your weight.
If you ARE actually burning as many calories a fit bit says in JUST exercise, then I can see how you could easily still lose weight eating 2K. It puts you at around a 600 calorie a day deficit.
FWIW You can actually exercise yourself into metabolic shut down the same way you can diet yourself to the same place. That's probably why its telling you to eat more. So, it actually IS playing nice! ;)
But, like I said, I'm not real familiar with Fitbit. Could be its just giving you an inflated calorie burn? What type of and how much exercise are you doing?
Calorie requirements for weight loss, maintenance or gain is based on age, height, weight and activity level. If you are really that active then your body very likely needs those calories to function properly - and that would include burning fat. There's no magic calorie number. It's different for everyone.