Voltage Doubler - Charge Pump
Now since we already had 3V across the first capacitor with respect to
  ground, it somehow doubles to 6V now?


No, the voltage across the first capacitor remains at 3 volts in that instant but, due to the clock signal rising to +3 volts, it lifts the capacitor up (both plates) by 3 volts so, there's now 6 volts on the upper plate with respect to ground and 3 volts on the lower plate with respect to ground. There is no net charge change on the capacitor in that instant - it still has 3 volts across it.