One requirement is that the sensor should be invisible (hidden) to the patient.

There is a thing that look like a small black cylinder called a "bedraiser"
Make 4 such, one with a loadcell and nobody will be the wiser.

in-bed patient weighing scale which works in the same way you have explained. The outcome is not encouraging due to the movement profile of the patients
That will definitely make a "real" scale flicker, but the differential between a person lifting a leg and dropping it (or whatever) should not be enough to upset an "occupied/not occupied" weight window.

Erik