This was what I was setting out to prove or disprove. Yes you need to fill up more often and if this requires a detour to the petrol station it will not mean much of a saving. But if like me you pass a petrol station it is not a problem filling up more frequently.
The idea is that you run the car in the lower half of the tank.
As you pointed out massive, a full tank is only full for the start of the journey.
You will save in real terms 1/4 of the weight of a full tank of fuel (because my maths tells me that the full tank empties therfore losing 50% of the 50% weight saving - I'm prepared to stand corrected on this one.) If you have a small fuel tank there probably isn't much in it, but if you have a 70/80 litre tank this becomes an interesting excercise. My tank is about 45 litres and I managed to save a couple of MPG!
It would be interesting to see what happens if we fill up the tank each time it gets half empty - pushing this theory the other way. The lesson I think is to let the fuel level run right down before we fill it up again!