Yes it's true. Think about cars: the larger/heavier a vehicle is, the more gas it takes to go the same distance than a smaller/lighter car, assuming the engine, etc. is the same. The heavier something is, the more fuel it takes to operate it.
But, don't let that discourage you. The smaller you are, the less you have to lose. If you think about it as a proportion rather than an absolute number, it helps. If running 30 minutes when you are 200 pounds burns X% of your calories, then running 30 minutes when you are 150 still burns X% of your calories. That is a large generalization, but it's a helpful model to think about.
The other thing to know is that different tissues in your body require different amounts of fuel. Fat is the least metabolically active tissue, so it takes fewer calories to sustain it than your organs or muscles, for example. So, as you lose fat, the % of your weight taken up by fat decreases, and that gives you a slightly higher burn rate per pound, so to speak. For example, if a pair of identical twins had different body compositions but weighed the same, the one with the lower fat / higher muscle ratio would need MORE calories than the other with the higher fat / lower muscle ratio. The difference isn't huge, but it's there. This is one reason strength training is so important -- if you increase your muscle mass, you boost your metabolic rate and you'll burn more calories than if you simply lost fat but did not add any muscle. In addition, one reason crash diets are so metabolically harmful is that the extremely low calories cause you to LOSE muscle along with fat. Low-carb diets can have this effect, as well.
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