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Extra weight, whether it is from a full tank, or passengers, affect neither air resistance (the main cause of fuel consumption at high speed) nor the amount of fuel needed to turn the engine over. Nor does it significantly affect rolling resistance provided your tyre pressures are correct. All it affects is the amount of fuel needed to accelerate up to speed and to climb hills. A half tank of fuel weighs about 20 kg, roughly 1 to 2% of the vehicle net weight. This is the maximum extent to which it will increase fuel consumption. Provided you plan your driving to minimise the use of your brakes, it will be effectively zero.
Over 50 years of regularly keeping a check on fuel consumption, I have never been able to detect any change due to the weight in my vehicle - initially a Lambretta scooter (where a passenger represents a huge percentage increase in weight) and subsequently a variety of cars. Indeed, some of my best results have been had on holiday with very heavily laden cars. My experience is if you minimise brake use (DWB I believe you call it), the presence or absence of even as much as 100 kg has no significant effect on fuel consumption.
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