You're putting 5V across roughly 2.5k ohms, which means you're putting 2mA through your DUT. You're seeing noise of about 4 ohms peak-to-peak, which corresponds to 8mV p-p voltage noise. That's much higher than I would expect, especially if the 6221 is configured to use the 200mV range for the DUT measurement, which it should be for minimum noise. Perhaps you're picking up noise from somewhere else? Do you have big current spikes going on somewhere nearby, or large voltage steps? If you can post a picture of an acquired waveform at a high sample rate, that might help us figure out where the noise is coming from.
2. The tolerance doesn't affect the fluctuations, just the accuracy.
3. Yes, a higher voltage (more current) would improve the signal-to-noise ratio for a given noise level. For example, if you used a 250-ohm reference resistor, your nominal voltage would increase from 6mV to 60mV, and the 8mV noise would correspond to a 0.4 ohm variation instead of 4 ohms. You have to be careful not to increase the current so much that the resistors heat up, though, as that could cause them to change value a little. For example, in my 250 ohm example, the 250 ohm resistor would have 20mA through it and 5V across it, causing it to dissipate 100mW. That would make it quite warm, and its value would fluctuate as random air currents change its temperature.
4. As long as you measure the voltage across each resistor close to the body of the resistor, wire resistance shouldn't cause a problem. The 6221 pulls very little current from its analog inputs.
5. The +5V source should be fine as long as it's quiet. But any noise on it will cause a change in the measurement. It might be worthwhile to try replacing the +5V with an analog output or some other independent voltage source for the resistance measurement, at least as an experiment.
Averaging is a perfectly acceptable thing to do, but it's best to try to minimize the noise before you resort to averaging.
Chris
