I needle dropped a record with and without the weight, then inspected the spectrogram for any changes. It will be very difficult to do null type testing with an analog rip, so all I could do was manual inspection.
This example is for something different, but the basic idea is the same:
Let’s assume the following spectrogram is with the record weight installed:
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Assuming this spectrogram was recorded with the weight off, any changes should be evident, similar to the differences observed between this spectrogram and the one above:
View attachment 459354
To be clear, the previous analysis compared two different masterings of the same song. The main point is that I would use a similar approach to identify any differences related to the record weight. The previous comparison shows clear differences, and I would be surprised if we observe anything similar with your recordings, as I did not notice any significant changes when I did my original test. This was also before I had AB Metric enabling me to measure other characteristics too.