Humm... Piper Cherokee 180, weight 1230 lbs empty, 2400 max, fuel consumption 8-10 gph. Boeing 747, weigh 128,700 lbs empty, 255,000 max, fuel consumption ~3600 gph (or about the weight of 10 Cherokees).
So yes, I think it's fair to say that heavier aircraft burn more fuel :-)
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