From experience with a similar aircraft type (steel rod gear also made by Langair Machining, the source of standard RV gear), the gear flexes upward, aft and outward as weight goes on the wheels.
If one is using bathroom or similar "spring" scales, these non-vertical loads can create very significant errors in measured weight. I thought I would be smart and put the spring scales on 4-wheel carts. Even this solution didn't produce sufficiently little rolling friction to completely alleviate side loads on the scales. It wasn't until I went to full strain gauge (load cell) scales that I was able to overcome these errors.
With respect to measurement of gear stations in "weight on wheels" vs "flying" condition, the answer to the question posed above is actually pretty simple.
We don't care one whit where the wheels are when we're flying, nor does the airplane. What matters is that we calculate the balance point of the aircraft. We put scales under the wheels and measure both the weight and location of the scales. This data then is compared to the location of the Mean Aerodynamic Cord (MAC) of the wing.
If one thinks about this for a moment, we could, in a perfect world, place one scale under the very tip of the spinner and one scale under the very tip of the tail (assuming the wings stay level because we built an aircraft that's perfectly balanced laterally). We would then do the math on the position of these two scales and the weights they read in order to come up with an Empty Weight Centre of Gravity.
Because we relate everything back to MAC, where the scales are located is of no great importance, as long as we measure exactly the location of those scales.
To another of Bob's points, side loading on the scales can introduce very significant errors in calculation of C of G, simply because that side loading can cause some scales to read highly inaccurate weights.