Analog sensor reading and calibration
You are correct: analogRead() returns a value indicating the proportional voltage of the input to the Analog Reference Voltage, which is either the supply voltage, 5V or 3.3V, or another value depending on the Arduino you're using and your settings.

IF you are powering the Arduino with the same battery as your sensor, as your battery's voltage drops below the Arduino's regulated voltage, if it's still high enough to power the Arduino, the analogRead() function will continue to return a proportional voltage between 0V and your battery voltage.  So there's no need to multiply the result by a constant as this is "automatic".

However, if you're powering the sensor from a battery and your Arduino from another source, you would need to know the battery voltage and adjust your analogRead() value proportionally.

Use a multimeter to ensure the voltage being fed into the Arduino is indeed changing as expected. 

Also, please show a diagram of your circuit if possible.