Why does an RTD sensor circuit use a reference resistor that is 4x the RTD value?
It may be some ratio that they think works okay with their chip. To my judgement it represents far too high a measurement current. For example, with a PT100-DIN the measurement current is 4mA at 0°C and 3.1mA at 400°C (ignoring switch resistance and leadwires).
That represents self-heating of 1.6 to 2.4mW, which represents about 1°C error for in typical thin film element in air at 1m/s.
Typically we'd prefer about 1/10 that current (1/100 that dissipation, and 1/100 that error in the reading).
I would not use this chip for any application where accuracy is important unless you really  understand the consequences in your setup. It is disturbing that they don't even mention it in the datasheet. Even in the olden days when getting low drift front ends was much more of a challenge, 1mA was considered about the limit for a PT100.
I suggest looking to other suppliers such as AD or TI.
P.S. In my example (0-400°C) about 36% of the ADC range is used (the span changes with the RTD temperature) so you get more like 13.5 bits resolution out of the ADC than 15.
Anyway, you are investigating noise. It's typical (!) 150uV RMS over Nyquist according to the datasheet. Near room temperature for a PT100 that's about 0.17°C RMS (so maybe 1°C p-p). At a more reasonable current, all that voltage noise would be a proportionally higher number of degrees, of course.