You can never solve drift or variations because of battery state, temperature, moisture, ... Just reduce the effect.

If using a current source, that source will not be perfect. It may not produce exactly the same current through the full voltage range, i.e. the full resistance range. And it will contain components that will age and will be affected by temperature. And the ADC will not be perfectly linear. And it will have an offset error and a scale error. And your voltage reference for the ADC will not be perfect. It will be affected by battery state, temperature, age, ...

You can reduce the effect of some of these problems by measuring the quota between the unknown resistor and a reference resistor. As usual, there are more than one way to do this.

Another thing to think about is that if you need to measure low resistances then you should consider a four-wire setup, where you have two wires for the current through the resistor and two wires for measuring the voltage over the resistor.