As the CG is moved forward, down force on the tailplane must be increased to hold the nose up, consequently increasing both the load on the wings (=greater induced drag) and parasite drag from the elevator. This will reduce the ratio of power to speed, therefore increasing fuel consumption for a given distance. IOWs, a forward CG will reduce the range. Some FBW A/C move fuel between tanks to keep the CG located at the CP (neutral stability) to conserve fuel.