What factors cause a turbine aircraft to have decreasing fuel burn over time? Consider a fictional aircraft with a fuel schedule similar to the following:
1st hour - 10,000 (lb or kg, doesn't matter)
2nd hour  - 8,000
3rd hour  - 6,000
4th* hour - 5,000
 * and subsequent

As we can see the fourth hour of flight burns only half the fuel of the first hour, so fuel consumption is a function of time.  Is the decreasing weight of the aircraft as fuel is burned the only reason for this increase in fuel efficiency, or are there other influences?  For example if a jet launches with half tanks versus full tanks, would you use the same 1st hour fuel schedule?
I may be way off base here, so if there are fundamental errors in my question, please correct me.
Per this paper:

Fuel consumption increases (approximately) linearly with aircraft weight, because weight corresponds to required thrust and thrust corresponds to fuel consumption.

The paper lists other fuel consumption factors as well.  But, as you suspected, aircraft weight is a dominant factor.