TheFlyingSquirrel-
That thing is a vertical vibration absorber, designed to "twang" probably at 4 per revolution frequency, kind of like a person standing on a diving board can make the board bounce at its natural frequency. It is resonant at the frequency, and so it absorbs those vibrations from the surrounding structure. It is very effective, that kind of absorber is used in the industry quite a bit. If it is not tuned right, that area of the cabin will feel like a rocky road. Two absorbers like that are located in the UH-60L near the pilot's step. The stiffness of the diving board and the amount of lead are selected to make it "like" the 4 per rev (which is probably about 21 to 25 Hz).
The place near its mount that is to be inspected is where the vibration gets passed through, so it is subject to high stresses, and thus the crack inspection.
I think I see a place on the weight for a vibration pickup to be mounted (the circle with a hole). If so, this is probably used at the factory to fine tune the absorber by reading how much it shakes in flight, and adding or subtracting weight until it is peaked out.