Here you see the pwm values up to 255 (flow doesn't start until around 80 or 90), and voltage read from a VOM across the output.
There will always be a minimum voltage required before the motor can operate to overcome friction and load. This will be dependent on the specific motor.
The flow from the pump also shows a very similar curve (pump output v. voltage is quite linear).
I suspect this is mostly a shortcoming of the meter being used to make the measurement. Unless it is capable of and includes circuitry/firmware to perform 'True RMS' measurement I wouldn'd put too much faith in the accuracy of your data points. A basic DVM is designed to read pure DC which a PWM signal is not. See if you can borrow someones DVM with true rms capablity and see what the data points look like with it.
It seems to me that voltage out versus pwm values should be quite linear, but it's not. Why?
See above answer.
Lefty