How can I increase resolution for current sensor?
In default configuration, the Arduino's ADC has a range of 0v-Vcc (5v or 3.3v depending on the model). If you are sure your input voltages will always be way lower than Vcc, spreading the ADC's resolution over that range is a waste of accuracy. What you need to do is to properly configure your analog reference voltage.

Basically, this is a way of telling your Arduino "instead of spreading your ADC's bits over a range of 0v to Vcc, just cram all that accuracy between 0v and [refVoltage]."

So:


Measure the highest analog output your sensor will give.
Setup a voltage divider to output a little more than that
Connect the voltage divider's output to the AREF pin
in setup(), declare analogReference(EXTERNAL);


And that's basically it. As noted, in this specific case you'd probably be better off buying another sensor altogether. However, you won't always have that luxury, and knowing how to set the analog voltage reference always comes in handy.