In the Linear Technology AN 105 on current sensing one can find the following circuit.

I am wondering what the purpose of the 200 ohm resistor on the inverting input is. It appears to have no effect.

Note that in the following paragraph a virtually identical circuit is presented that is lacking said resistor:

As a side issue: is there any downside to sizing the 200 ohm input impedance resistors significantly larger, e.g. 10k? (Keeping gain constant.) The aim would be to reduce the current the opamp draws from its supply to drive the BJT.

Edit 1: cf Kaz's comment

Edit 2: Johnson noise