That is true for low speeds, but for 500 mph your lift is much greater than your weight. You may stop your engine (0 Hp), center your controls. and your plane will start climbing for a while.
At these speeds you need to counteract your lift with your elevators to keep flying at level. The heavier plane will need to compensate less than the lighter one, that should mean more drag from the controls of the lighter plane to keep flying at level. At the end that may imply a slower top speed.
All these considering that less fuel doesn't imply a redistribution of the weight in reference with the CG.