Help, not losing weight.

So I started my weight loss journey over 5 weeks ago, I'm not losing weight. I have lost 2 pounds and not measurement loss. I am feeling very discouraged. I exercise almost daily, and on average burn at least 600 calories a workout. It seems to me that with my healthier eating and exercise I should be seeing numbers drop.
Food is a struggle for me, not eating too much, but too little. I find it very hard to eat 1200 calories a day, and that isn't including what I am burning! I could really use some support here...I am feeling very down on myself today, which seems to happen at least once a week since I started this because I am seeing no changes. I do feel stronger, which is great...at least something is changing.

So lets do the math as to why no weight loss.

You eat, lets be generous and say 1200, though less than that.
You exercise on avg daily 500, though you said more than that most days.

That leaves your body with 700 calories of food for basic metabolism for functions of life, BMR.
If that is all it has available, some stuff is left not done, and it slows way down, to that level. That effects all daily activity burn. Which of course means you no longer burn 500 avg for the workouts, but close enough since we underestimated that anyway.

You seem to have daily activity including exercise what would probably be considered between Moderate and Very Active - about 1.63 multiplier.
So true suppressed BMR of 700 x 1.63 = 1141 daily activity burn.

The body will adjust that up as it balances out though. So you are actually eating at maintenance level, if you could even eat 1200.

Just want to be clear that you are going the right direction trying to get suggestions.

In the meantime, to save the muscle you've got, you really should stop working out. You are not doing yourself any favors right now.

You aren't eating enough for metabolism to increase because of it, it can't. It just means more things the metabolism would normally take care of, it can't. Your muscle can't repair fully, can't build more, can't store glucose for energy, because diet is probably in deficit for providing what you need each day, muscle breakdown is occurring to offset lack of blood sugar. Fat burning is still going on, but at such a slow rate because your general daily burn is so low now.

This is not a good direction obviously, so keep eating, great suggestions given to get your body going again.

You can get out of this slump. Isn't it strange your assignment is to eat more so you can lose weight.