Understanding to isolating sensor input capacitance
Notice the asymmetry. P$GND is driven by an output, presumably with a reference voltage from U1. Presumably U1 isn't suitable for driving capacitive loads, a lot of opamps can be unstable driving capacitive loads at unity gain. 

So without R3, U1 may oscillate instead of generating a steady voltage reference.

P$SIG is only an input, so has no such problem.