Unless I have totally misunderstood the question... a weighing scale measures weight. It gives the value of the force pulling you down to Earth. But then you can use F=ma to get the mass. So, the difference between mass and weight is important, but not so much in this simple situation.

To me, the thing they measure is mass, not weight, as the unit is in kg.

Mahtab Shihab that depends on the instrument itself. But as you know the acceleration due to gravity there is not really much difference. The scale is based on the force and then in suitable units that could be equivalent to the mass - assuming you are on the surface of the Earth!