Well doesn't the aerodynamic shape and the weight kind of "anchor" the plane so that it doesn't get blown off course by some winds (and thus having to burn more fuel to stay on course of fly back on course)? i.e. when I throw a piece of paper vs. a full bottle of water, the bottle of water will likely travel farther and faster even though it's much heavier than the piece of paper.

One could argue that this effect cancels out the extra fuel burned.