Presuming an engine is equally efficient at all speeds (which is very incorrect, but makes it almost possible to figure out a solution), then "fuel use" = "power required". And if the rig is not accelerating, then "power required" = "total resistance to moving". This "total resistance to moving" is composed of "air resistance", "rolling resistance" and "mechanical inefficiencies".
Of these, weight really only effects rolling resistance. Technically, on a one-way trip, the down-hill journey will require less fuel - but for any round-trip, the amount uphill is compensated for the downhill part.
Rolling resistance is the major component of "total resistance to moving" only at low speeds. Like less than 30 mph (48 km/hr). Once speeds get above that, air resistance very quickly becomes the dominant component. The air resistance is related to the air speed squared. So all else equal, changing the weight will have almost zero effect on fuel use at highway speeds.
The other situation where weight is a factor is acceleration. The more times you have to speed up, the more fuel you will use. Minimum fuel usage when accelerating will be when the engine is operating in it's peak efficiency RPM range. That varies depending on the engine. The suggestion to monitor fuel use with a ScanGauge or the like (if your vehicle can connect to one) is possibly the easiest way to figure out where your engine is most efficient. But that will not help when cruising on the highway, only when speeding up. (stop sign, stop light, on-ramp, etc)