Do you know a new Japanese battery? It's AA size, but it's so strong, only 3USD each.
If you use a 6V motor, you also can use 3 V supply, it still works. I cannot get the strongest torque of the motor, but I'm sure it will works. As you use PWM for 6V motor, at 50% duty cycle, that is, you seem to apply 3V to the motor. Yeah, there are some differences, but in a small light application (not a micro application) dont care muchie about it. It works.
If your application is a microbot, I think you have to use servo or RC motor. RC motor, in fact, it's used for remote controling, but if you use RC, it's so tiny.