> If you eat 4k calories but burn 5k, you'll lose a lot more weight than if you ate 1000 and burned 2000.

No, you’ll lose less weight (I mean, assuming the difference in what you are burning is from exercise, if you find a way, e.g. by some chemical intervention, to kick your metabolism up to burning 4× your baseline amount without doing additional exercise, this doesn't apply), because you have the same calorie deficit and more of the weight you lose (unless you are in fairly great shape to start with, more than 100% of the weight you lose!) will be fat, and it takes a greater calorie deficit to lose a pound of fat than a pound of muscle.

OTOH, most people want to lose fat and avoid losing muscle, so this is a good thing, but its not more weight loss.