Increase resolution of voltage divider
To achieve this, you have two main options: You can use an opamp, which can remove the DC bias and amplify the difference, or you can use a differential ADC.

For the former option, Op Amps for Everyone is an excellent reference. The differential amplifier in section 3-6 is an example of what you want; you can generate the reference voltage with a resistor and zener diode, or a resistor divider from a known input voltage.

The other option is to use a differential ADC. Presumably you're using a microcontroller to digitize this, and most microcontrollers support differential inputs. Input the reference voltage for the negative terminal and the divided voltage for the positive terminal and you're sorted.