Problem with reading values from an analog accelorometer
The output impedance of 32 kohm can be a significant problem when attached to the ADC input on the MCU. Table 24 entitled "16-bit ADC operating conditions" states that the input impedance is typically 2 kohm and this will screw up any measurement from a source that has an output impedance of 32 kohm. 

You might get away with a parallel capacitor - the sensor data sheet specifies there must be a minimum of 4.7 nF on the sensor output so have you done this? Alternatively you might need an op-amp buffer.

The table in the question suggests that you might be using a PGA in front of the ADC - please confirm that you have enabled this because it makes things easier but you will still need a 4.7 nF capacitor and normal decoupling across the power rails.

Reading further down the PGA table suggests that the analogue source impedance should be typically 100 ohm and this is way lower than what the ADI device is. I think a buffer might be a good idea.