I've designed a Galvanostat (meassures the voltage drop vs time in a sample while applying a constant current) and the final ADC conversion shows some extrange behaviour. Instead of showing a continous variation in the voltage meassured, it show a plateau-like conversion. Meaning, the conversion is constant for a few samples, forming a plateau and providing the exact same 16bits value, and then jumps to the next voltage value. This behaviour is more visible as the rate of change in voltage lowers.
The experiment was carried with a 100ms sample rate, but my software can change that value to whichever I want. The conversion is made with the full 16bits allowed by the IC. The voltage value shown in the graphs is the voltage drop in the sample, which is the value given by the ADC after some tranformations (an offset and a gain). The plateaus form at exact 10mV jumps and that is, in DAC values, an exact 64. That value is a power of 2, so it's too much of a coincidence, isn't it?. I can show you an excel sheet with the saved data from several experiments, and the same exact DAC value (with +-1 variations) is read several times in a row. It's impossible that the signal is so stable that a 16bits DAC reads the same value 4, 5 or even 6 times in a row or show only a 1 or 2 bits difference in 10 consecutive meassurements.
I tried changing the ICs in the circuit, changing the experiment conditions and many other things, but the problem seems to be in the way the ADC reads the data.
I was using a multimeter to read the in voltage and, strangely enough, while the multimeter was connected, this behaviour disappeared and the conversion went as expected, but a bit of noise was added. I suppose that the multimeter pressence stabilized somehow the ADC reading, but i wasn't able to recreate it on my own.
Here are some images of my circuit and the curves I got from different same-conditions experiments. The one in black is meassured with the multimeter connected. It is of note than the other three show the exact same plateaus at the same voltage values. I'm only showing the last past of the signal path, which I think is the only part relevant for my question.
Can anyone please give me a hint of what may be happening?

