IMO ~ if you aren't feeling hungry because you aren't eating enough, your body has gone into "starvation mode." It's where the body thinks it won't get enough food so it's holding on to what it gets and allows itself to no longer feel hungry even though it needs more.

If you aren't losing, which you aren't, it's because your body is holding on to everything it gets.

I was recently homeless, couldn't cook anything and my body would feel full after a small sandwich every other day. It was definitely not enough for my body. I had to force myself to eat once I got into a situation where I could actually eat. You need to eat more before your body will understand that it will get food when it needs it.

I'd like to see your typical day's eating, if you think you could post a menu - it might help people focus their advice. I am a little skeptical that you can eat 1000 calories a day and exercise and not feel hungry. How are you estimating your calories?

Assuming that your estimates are correct, though, try adding some fat. Put a tablespoon of olive oil on your vegetables. Or, if you are eating low-fat cheese, switch to full fat. Or, have a (measured!) portion of nuts for your afternoon snack.

Dietary fat is not your enemy, especially if you are only eating 1000 calories a day.

Finally, remember that there is a long time constant before you'll see the effects of any change. Changing your eating for a day or even a week doesn't tell you anything about how your body responds. You have to incorporate changes slowly and observe your body's responses - your hunger, energy, and weight - over the course of at least several weeks to know whether something works for you.