Measuring tiny voltage variation with Arduino ADC handing the rapid changes in control algo
A 10-bit ADC at 5V has a resolution of 5mV. Your sensor has a sensitivity of 100mV per inch, which you reduce by your resistor divider to 50mV per inch. That means 10 ADC counts per inch. This isn't much, especially when you think that you'll always have some noise in your readings.  

If you're interested in only a small range, like the 1.99V..2.09V, subtract the 1.99V from the input using a difference amplifier and amplify 50-fold to get a range from 0V to 5V.  

  

If R1=R2 and R3=R4 then


  \$V_{OUT} = \dfrac{R3}{R1} \times (V_2 - V_1) \$


I would still use a low-pass filter in software to filter out the noise.