The superconductor is "levitating" by being repelled (magnetically) by the platform, which is in turn being repelled (physically) by the scale. If either of those were not true, the scale and/or platform would start moving towards the center of the earth due to gravity.
Really, all it is is a fancy stack of objects.
Weight is the thing we can directly measure as the masses of the earth and the object interact together.
So if you imagine the scale to be a simple spring and a calibration scale of spring compression distance mapped to known weights then it’s pretty simple to see that the stack of objects act on the spring all the same despite the magnetic effect between them.
The masses are being attracted towards the earth, and the spring is the thing stopping them, when they are at rest sat atop the scale the spring compression is balancing the weight force of the masses gravitational attraction.
The foundations of a maglev train track obviously must be able to support the train tracks and the train on top of it, even if the electromagnets are engaged and the train is levitating.
(Every time I've done it though it was the other way around, I put a superconductor disc in a petri dish and poured the nitrogen on and then floated the magnet over the disc.)