Burning 1000 calories a day does not guarantee weight loss. Whether you will lose weight or not does not only depends on how many calories you burn per day, but also depends on how many calories you eat. The rule is when you eat less than you burn, you will lose weight theoretically.
Say you burn 1000 calories and eat only 800 calories a day, you create a calorie deficit of 200 calories. So where does your body get these 200 calories? From stored sugar and fat. If you keep doing this, the stored fat will be burnt gradually. Then you will get slim.
Say you burn 1000 calories and eat 1200 calories a day, you get extra 200 calories. Where do these calories go? Most of the 200 calories will store as fat in your body, so you gain fat day after day by eating more than you burn.
If you want to know how many calories you need a day to lose weight, use the tool to calculate by clicking the link.