Current Sense Resistor – Choosing Between Series or Parallel for Switch Current Sense Resistor

The 200 Ohm resistor on the inverting input has no effect for an ideal op amp, which has no input current.

But real op-amps require a (very small) bias current, and also have offset currents flowing from the non-inverting input to the inverting input.

Because of the offset current it's best practice in a precision circuit to have equal impedances feeding the two inputs of the op-amp.

In the case of the LT1637 with 5 V supply, the offset current could be as high as 15 nA. If the input impedances weren't balanced this could cause an error of up to 3 uV, corresponding to an error in the current measurement of 15 uA.

is there any downside to sizing the 200 ohm resistors as e.g. 10k?

There's no real issue with a small change in that resistor value (for example to 211 Ohms or something), but no advantage either.

If you were to increase the R1 resistance to 10 kOhms, I'd start to worry about Johnson noise generated by the resistor. But I haven't looked at the effects carefully, and of course the maximum acceptable noise depends on your system-level requirements.

I like using the closed-loop Hall effect LEM current transducers for this sort of application. They're a lot cheaper than a genuine current probe for a scope (only about $20 or $25), have excellent accuracy and bandwidth from DC up to a couple hundred kHz.

The particular one I've linked has a +/-6A range, but you can put a couple loops through to get +/-3A full scale. Just feed it a reasonably clean +5V and Robert's your uncle.

If you want to make more of a project of it, you can offset the output with differential output between the LEM and a 2.5V reference, or actually subtract it with an op-amp and bipolar supplies, but for most purposes, just adjusting the scope zero will do the trick.