voltage drop across analog multiplexer
Pay attention to Andy's comments on the dynamic input impedance of your ADC, which is almost surely an issue given your measurements but there is another important issue. 

You state the Ron to be 125 ohms, but that's the typical value with a Vss-Vee= 15V. Your situation is completely different, and if you are actually using a CD4051, it will only barely operate properly from 3.3V and Ron is not guaranteed at all (it's only guaranteed to be less than 1050 ohms at 5V, and 1.2K at 85°C). Nor is even a typical figure given. You are well into here be dragons territory.



I suggest you add a buffer (op-amp voltage follower) after the multiplexer to isolate the dynamic loading of the ADC (typically it's a linear function of sampling rate) and substitute a 74HC4051 for the CD4051.