suppose you want to measure 0 to 10mv signal,to keep it in 1 volt range if you use 1volt reference in case of 8bit adc gain is 100,10mvx100=1volt
now let us say signal at input of amplifier is 1 to 30 microvolts after gain of 100,at input of adc is 100microvolts to 3mv,with 1 volt reference as you say resolution is 3.9mv,you are unable to measure signal from 1 to 3mv or from 1 micro to 30microvolts.

now consider a case of 14bit adc with 5volts reference,amplification factor in this case is 500 to attain 5volt scale and 1 to 30 microvolts signal will be amplified to 500microvolt to 15mv,with 5volts reference 14 bit adc will give 305micro volt resolution,and signal from 500micro volts to 15mv or from 1 micro to 30microvolts can be measured,which is
not possible with 8bit adc even with 1/2volt reference