A question on limits of resistor vaules in an op-amp input
Stray noise is voltages and currents induced in the wires due to electromagnetic waves that are all around us. Stray noise can come from external to the board, but it can also come from within the system. Logic gates and drivers switching etc.

When such noise is in the vicinity of a wire it will try to induce a voltage in it. If the wire has a high resistance to your ground reference, the voltage the noise can create is significantly larger than a wire with a lower resistance.

The input of the amplifier is high impedance. If R1 and R2 are also high impedance that makes it is easier for electric fields to generate voltages on your input and interfere with your circuit. 

That can be illustrated as below. 







simulate this circuit &ndash; Schematic created using CircuitLab

You can see that that noise has two opportunities to enter your signal path, before and after the input resistor. 

Ideally the source impedance of whatever is driving your circuit should be quite low. This is the case for the output of most op-amps. With a low input impedance driver the voltage divider of the noise on the left side does not leave much voltage noise on the left side of R_Input.

If your source impedance is higher, that is, from some sensor, voltage divider etc. Then significantly more noise will appear on that side. That is why it is important to keep the sensor as close to the first input pin as you can, use twisted pair wires, shielding etc, or to actually add a unity gain buffer close to the sensor.

With no feedback on it, the op-amp input pin impedance is normally very high impedance. If R_Input is high the voltage divider on the right leaves significantly more noise on the right side of R_Input.

The worst case would be leaving the resisters out entirely. "Infinite resistance" (Not really but we will go with that for this argument.) At which point your trace becomes a nice little antenna. 

ADDITION: The OTHER reason to use lower values.

Not shown on most schematics because it is not an actual part is trace impedance between the trace and ground. This is mostly capacitive and resistive but also has an inductive part too, especially on long traces and wires.







simulate this circuit

As you can see that creates a low-pass filter on your signal. The higher the input resistor value you chose the more you will cut off the higher frequencies of your signal. 

Because it is an impedance there is also some signal loss due to the resistive part. The bigger your input resistor the more the loss.

The Balance.

From the above you can see high value resistors add all kinds of issues. Lower is better. However, low value resistors also means more current consumption since your drivers need to work harder. The trick then is to balance the trade-off between noise and frequency response performance against acceptable power usage.