Got very low current from PWM in Arduino
You are using the transistor as an "emiiter follower" so the base current is what it needs to be to satisfy the beta equation of the the transistor for the current through the emitter. I don't know what emitter resistor (or LED) you are using so I can't tell you what current to expect but 40 uA x beta (say 100) gives an emitter current of about 4 mA.

Given that the base can be as high as 5 V and it'slikely that the LED doesn't need more than 2 volts to operate, using an emitter follower (common collector) is a perfectly good way to deliver the current needed.

If your meter is set to read DC current then it should adequately cope with the superimposed PWM signal and read fairly accurately. Also, in this type of configuration you don't need a base resistor (just trying to allay what has been said in comments).