The purpose of an afterburner is to provide additional thrust, and it is obvious that more fuel is needed for that.
But that is to be expected independent of an afterburner. That more thrust needs more than a proportional increase of fuel may be the case because the thrust increase needed per speed difference is not linear¹.
The reason to build afterburners may be that stronger jet engines can not be build with the same mass or volume. Or that a stronger jet engine is not useful in standard use, for example because the fuselage would overheat.
Doubling the speed increases the fuel usage by more than double I would expect, purely based on aerodynamics, independent of the engine.
Is the fuel usage for increasing speed greater with an afterburner than with a stronger jet engine? How much? Why?
¹ For spaceflight, that is true according to special relativity.