[Retric]

It's more complex than that. The floor an object sit's on is also attracted to the moon so you would need to look at the difference in attraction over the size of the device.

However, the earths crust deforms a few cm due to tidal forces. Which weekens local gravity. Aparently you can measure tides in a trees sap so detecting them on a small scale is probably possible. (My google fo is failing to find that one though.)

[pyrois]

It is certainly more complex than that, but I think that a back-of-the-envelope calculation like the one above is more than enough to strongly suggest that getting a solid object to remain in place when the moon is above it and not when the moon is below is very unlikely to be feasible.