Do aircraft use the majority of their fuel to overcome friction?
No, the majority of the fuel is wasted on inefficiency of the engine. 

Internal combustion engines like turbine engines are not exactly energy efficient. Most of the fuel is wasted by running the engine. Only about 35% to 40% of the energy from the fuel is converted to propulsive energy.  The rest of the energy from the fuel (~ 65%) is lost on heating up the atmosphere directly, excess kinetic energy in the exhaust stream, internal drag &amp; friction of the engine and producing noise.  

The remaining ~35% the energy is there to overcome the work done by drag. 

This drag can be split into lift induced drag and parasitic drag. 
It can also be split into pressure drag and friction drag. 
For simplicity assume that all the lift induced drag is all pressure drag, and all parasitic drag is friction drag. 

Aircraft usually cruise near the speed where drag is lowest. In such a situation, 50% of the drag is induced drag and 50% is parasitic drag. In practice cruise speed is a bit above the minimum drag speed, so the parasitic drag exceeds the induced drag. If our earlier assumption is correct, then over 50% of the drag would be friction drag. 

That would bring the total estimates to:


65% wasted
20% friction drag
15% pressure drag




For example the GE90, the engine fitted on most Boeing 777s, produces a thrust of 70 kN in cruise flight of 250 m/s at a fuel consumption of 1.08 kg/s.

The propulsive power delivered by the engine is $70 \cdot 10^3 \cdot 250 = 17.5\cdot 10^6 \textrm{W}$. 

Jet fuel has a specific heat of $43.15 \cdot 10^6 \textrm{J/kg}$
The energy consumption of the engines is thus:

$1.08 \cdot 43.15 \cdot 10^6 = 46.6 \cdot10^6\textrm{W}$

That gives an efficiency of 37.6%. This may seem poor but it is one of the most efficient engines available today. 



Data sourcePDF for thrust, speed &amp; consumption: