Do afterburners use excessive amounts of fuel? 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.
Yes the specific fuel consumption of the afterburner, lbs of fuel used per lb of thrust, is much higher than the core engine.  This is because the fuel is being added to a part of the engine where the air is less compressed, so the energy conversion is a lot less efficient. The bright orange flame coming out the tail pipe when in reheat is pretty much all that un-oxidized carbon fluorescing - wasted energy. See this article.

Fighters use reheat because all that extra power is available with minimal extra weight (the weight of the burner and additional fuel), but they can only exploit that power for short periods if they want to have decent range or endurance, so they are generally used for dashing somewhere, or to assist with maneuvering, or taking off with a heavy load.