Sio Uongo Soma Hapa mkuu!
One study by consultants Ricardo Inc examined the effect of extra weight on fuel economy.
Roughly, it found the fuel economy increases by between 1% and 2% for every 100 pounds (43.5 kg) of weight added inside the car. This figure does not factor in any extra weight outside of the car, such as roof racks, trailers or sidecars.
Suppose we took the upper limit, 2%, and assumed a full tank of 60L in a car that is rated at 8L/100km (a typical family car).
Crunching the numbers
Since petrol has a density of roughly 720 grams/L the weight of the full tank of fuel is about 43.2kg. So, roughly, your fuel efficiency will drop to 8 x (1 + 0.02 x 43.2/43.5), which is roughly 8.16L/100km.
As you drive, you use up some fuel, and hence carry less weight in the car. When you have used half a tank your fuel efficiency is now roughly 8.08L/100km: the car is travelling more efficiently than it was with a full tank.