Eating back exercise calories?

Okay, I just saw mention of this for the first time: "eat back HALF of your exercise calories."

Is that what I've been doing wrong? I've been eating ALL of my exercise calories (as determined by my heart rate monitor).

Just want to get more verification. Is this what people do?

I'm eating 1200 per day plus exercise calories at present, and totally stuck at the same weight for freaking ever. And yes, I use a digital food scale.