How is the cruise speed of an aircraft chosen?
The speed of the aircraft in cruise is determined by the forces in the horizontal axis: thrust and drag. Weight and lift are forces in the vertical axis; they do pop up in the horizontal axis, but are relatively tiny in cruise.

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At low airspeeds, induced drag is the dominant factor: this is the drag that is proportional to lift and weight. At cruise speeds, induced drag drops off and parasite drag rises quadratically with airspeed. It is drag associated with the aerodynamic shape of the aircraft. At any weight, the most beneficial shape is the one that aligns the fuselage best with the free air stream: tilt the nose up or down from the Angle of Attack for minimum parasite drag and drag will increase, at any speed and weight. Wind tunnel tests and Computed Fluid Dynamics are the tools used for establishing minimal form drag.

However, for straight and level flight the vertical component of lift must indeed match the weight, so one of the parameters of the flight state must be tuned in order to get zero climb rate. Changing cruise speed is indeed one of the degrees of freedom to change lift, but not the best one. In the aircraft aerodynamic axes, lift L is given as $$L = C_L \cdot \frac{1}{2} \cdot \rho \cdot V^2 \cdot S$$

S is wing area, usually a constant that cannot be changed during cruise. So the degrees of freedom to change lift are:


Change lift coefficient $C_L$: this is done by changing Angle of Attack, by pitching up or down. Doing so creates extra drag and fuel burn, the least amount of drag is generally with the fuselage aligned with the free stream.
Change air density $\rho$: fly higher or lower. This is what is done when the aircraft gets lighter due to fuel burned: at higher altitude there is less air resistance and less thrust needs to be delivered by the engine, improving fuel burn without slowing down.
Change V. Flying slower as fuel is burned is beneficial for fuel burn per hour - but it takes longer for the aircraft to arrive, so fuel is burned for more hours. 


So for varying weight, it is best to vary lift by varying altitude. Long range cruise aircraft would have the least fuel burn if they could gradually climb as fuel weight diminishes, however there are air traffic corridors which the aircraft needs to stay in. Cruise climb is done in steps instead.



From this lecture, which also provides equations for cruising at constant altitude (varying velocity) and at constant velocity (varying altitude). The latter wins.