I think it is likely your increased appetite is related to your increased activity level, unless the "hunger" comes during or immediately following exercise. If you burn more calories, your body is going to try to encourage you to eat more to replace what was lost. Bodies love homeostasis. They set a weight point and your body will try to maintain your weight at that point.

Your body will slow your metabolism if it senses you are cutting calories too much. This will result in harder to lose, quicker to return weight. If you work harder, your body will naturally tell you that you are not getting enough calories and indeed, you are NOT getting enough to maintain your current weight.

If you are staying under 2000 calories a day, you will continue to lose weight. A little slower than if you keep it lower but you also want to beware causing slow down in metabolism. The increased activity however should rev up your metabolism some so it may break even or close. Maybe it would help to figure out if (short term) you could get a weight maybe weekly to see what kind of loss you are getting at each calorie level.

Are you finding that your weight is going up again, or that you have stopped losing weight? If you are still losing weight, it may be that you are using up the extra calories, though 500 seems like a lot to use up. If you are getting hungry you could try eating lower calorie alternatives to whatever you are filling up with - a big salad with your favourite ingredients and a low calorie dressing in hot weather is very filling, and a big bowl of vegetable soup is good and filling in colder weather. It would be sad if you put some of that hard-earned weight-loss back on!

You may not like my answer but here is what I think.

More food is what not what your body needs if especially if your lifestyle is not very active. Probably it is the mental relationship with the food. Keeping your favorite foods around, buying low groceries, avoiding restaurants etc. helped me reduce my intake. I used to sit around at computers at work and at home and eat more. Now I get up early for exercise (for about 1.15 hr) but my food intake is reduced. It was because I told myself that I do not need more food for my lifestyle. I eat breakfast, a small lunch and avoid dinner (often snack on cereal). May be not everything ideal but it working for me. I am looking so much better than my profile pic.