neepie:
To measure this you don't need to use an Arduino.
Just hook your meter between the LCD backlight power pin and power.
That will tell you the maximum current the backlight draws.Thats what i did. when trying to pwm value 220 it gave me about 10mA.
It sounds like you are not using a direct connection to power.
When measuring power as I mentioned above there is no Arduino
involved (The backpack doest not even need to be connected to the Arduino board)
and so there can not be any pwm involved since it will be measuring
the current between a direct connection to power and the LCD backlight.