How does flight duration affect the hourly fuel consumption in heavy aircraft?
General Answer

The heavier the airplane, the more fuel it will burn in a given amount of time.  Therefore, if you takeoff with enough fuel to fly further, you will be burning more fuel in each corresponding hour than if you took off at a lighter weight to fly a shorter distance.

Example

I don't have performance information for the 747, but I can give you an example for a G-IV corporate jet.  Instead of comparing a short trip to a longer trip, I planned the same trip with different amounts of fuel in order to make the airplane heavier.  I planned the flight for the following conditions:

Flight Conditions


Fly from Los Angeles to Detroit, using the same route and average Boeing winds for July
Climb to and maintain the optimum altitude, with step climbs where appropriate

Trip 1: Climb initially to FL450 and stay there for the entire flight (the optimum altitude for this weight)
Trip 2: Climb initially to FL410 and then climb to FL450 2:32 into the flight (the optimum altitude the weight initially followed by a climb once the optimum altitude has changed)

Fuel:

Trip 1: Takeoff with enough to land with a 1:30 reserve - 59,000 lb. takeoff weight
Trip 2: Takeoff with max fuel, landing with a 5:39 reserve - 73,000 lb. takeoff weight
Taxi fuel is not included in the first hour burns, but climb fuel is.



Results

          Trip 1      Trip 2  
Hour     Fuel Burn    Fuel Burn     Diff
 1        4,212         4,844      +13.7 %
 2        2,536         3,088      +21.8 %
 3        2,411         3,123      +29.5 %
 4        2,163         2,103      -2.8 %  
 Total    11,722        13,558     +15.7 %   


Summary

As you can see, the fuel burn is significantly higher in the first 3 hours due to the additional fuel that we were carrying (and therefore the higher weight of the aircraft).  Hour 4 is almost the same because of the idle power descent used in the planning software.