Question about eating back excercise calories.

I've read somewhere that those people who are not exactly overweight NEED to eat back their excercise calories. I fall into that category. My question is: what good comes from burning calories doing excercise, if I have to eat them back again? (I really don't know much about it, that's why my logic may seem dumb)

Or do I need to eat the necessary calories to reach my daily goal, and NOT all my excercise calories in their entirety?

Also, kinda off topic, but starting tomorrow I will up my calorie goal to 2000 per day (apparently I was eating a dangerously low amount of calories). It is possible that my body was in starvation mode, since my weight has been stalled for a week or two, and I netted 1000 max for almost a month, without realizing how bad it was.

After increasing my goal, what should I expect? Temporary weight gain?

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