Angry,
In fact, more fuel is burned just to carry the weight of the non-stop fuel than is used making a refuelling stop. And if you then use a shorter range aircraft which will be structurally lighter with smaller engines etc, you reduce the fuel burn even more. So while aircraft are being designed with longer and longer (9.000 nm+) range, they are becoming relatively less and less fuel efficient compared to aircraft using the same technologies (light weight materials etc) designed for shorter sectors. Of course, making tech stops is more inefficient in terms of crewing, maintenance costs and user charges so it isn't necessarily more cost efficient overall than non stop.