Experimenting interference effects for different measurement systems
There is a power supply inside the function generator. With a power transformer to isolate (or float) the Function Generator output signal (your 10mv at 3Hz). When you use the 3-wire cord, you are grounding lots of pieces of metal, and the long cables likely are picking up 60Hz hum that does to ground, thus making the 10mV ride atop 60Hz power line trash.

Your very slow sample-rate (what is your sample rate) converts the 60Hz trash into apparently random spikes. The consistent (-) going trash polarity may come from the polarity of rectifier charge surges.

Friend of mine dubs vinyl records onto harddrive; the turntable has a 5th wire, which is a non-insulated copper braid tied to the metal tonearm and metal baseplate under the motor. The 2 cartridge channels --- left and right --- edit the tonearm in twisted pairs (not shielded) that run over and very close to the metal baseplate, before becoming coax-cables out of the turntable to the RIAA preamp.  If this 5th wire is dis-connected, the RIAA preamp outputs milliVolts of 60Hz. If the 5th wire is tied to the RIAA preamp "GND", hum becomes microvolts.

You have the challenge of learning to handle electric fields and perhaps magnetic fields, in a precision signal measurement system. 

One way to launch into understand is by drawing some sketches of what connects to where, including the cable distances/shield_resistance/shield_inductance, and then inject trash of various frequencies that need to find a RETURN path. All possible paths will be explored, proportional to conductance.