Hi,
It's decoupling. The vibrations are transferred from the cabinet contact to the stand. If the stand is hollow, it can cause all kinds of stuff. It's the same reason people have spikes on their speakers on carpet, and rubber feet on their speakers on hard surface. Decoupling. And you should notice it mostly, audibly, in bass like you did.
Another good way to isolate, without foam, is blue tac. It will decouple just as well, but also keep the speaker from falling off from a random bump. It's a better "long term" decoupling solution for a bookshelf on a stand.
As for measuring it, just do a sweep from 30hz to 700hz (+/- to your preference) in high resolution with your UMIK-1 in REW. Make sure to adjust the microphone height to the speaker at the same position after you add/remove the isolation foam so that it's recording as close to the same position each time so you can see the differences. Don't apply any smoothing. Post your two graphs.
If you're near a wall, based on what your graph shows, the next step is likely to apply treatment near by... but instead of doing it blindly, it's best to see what's going on with your response curve by measuring it (looking for nulls, modes, reflections, etc).
Very best,