Pontiac G6 - engine frequently revs up when trying to accelerate.

Pontiac G6 2010.  Lately when accelerating from idle, the engine revs up when I accelerate, pressing the gas pedal with moderate force.  The RPM will go up to 3500 or so.  If I back off it comes down but to gain speed I have to gently apply pressure to gas pedal or it will rev up again.  I usually back off the accelerator to let it come back down.  The best way to get up to normal in-town speed is to go very slowly from 0 to driving speed.  When needing to accelerate in a hurry the reving issue kicks in.  This doesn't seem normal.  It is especially likely to happen if the air-conditioner is on.  Turn it off, and it behaves better