A B747 Captain reported a fuel over burn on an oceanic flight that resulted in a diversion to an airport short of destination.

Narrative

Aircraft experienced a fuel over burn that stabilized between 6 to 7;000 LBS resulting in a precautionary fuel stop. The event began at the first fix after top of climb. I don't recall the exact numbers but we were about 1000 LBS down at that fix. At each ensuing fix the over burn steadily increased. We made the cost index correction for our departure weight and later adjusted it as we became lighter. Mach number and true airspeeds were within flight plan ranges. It had no effect on the rate of over burn. For a couple of relatively short periods we had a minor wind busts which were reported to Dispatch but they were not of such duration that would have adversely effected the over burn to such an extent. All members of the crew and dispatch were actively involved in the problem to no avail. Approaching the redispatch fix we calculated that we would be arriving at destination with just about FAR fuel of 16.7 if I recall correctly and the landing flow was to the East. We felt that landing on the east runway would more than likely result in a slowed and dirty approach to the airport; and we would be landing with far less that 16.7 and decided a fuel stop the prudent thing to do. Personally; I believe the airplane was heavier than advertised. I recall pointing out EPR settings that seemed high for our weight and altitude but I did not make note of them. The next time this happens I definitely will.