Usually the weighing machines have a platform under which there is a spring. The spring gets compressed. The amount x of compression is measured. This is multiplied by the force constant k of the spring. Then it is divided by the gravity g at the location. That gives the mass of the person standing on the weighing machine.
F = m g = k x
=> mass m = k x / g
There is also a force acting on the spring due to the weight of the platform, and the spring itself due to gravity. So the reading on the machine will be more than the reading.
There is a gravitational attraction force between the machine and the person standing on it. This force adds to the weight of the person. So, the actual force measured by the machine will be the weight of the person + attraction force between the machine and the person. So the measured value will be more than weight of the person.
But, the reading is displayed after taking into account the other factors. So the mass is correctly reported. The weighing machine is tuned/calibrated properly to take in to account these other factors and the location on Earth. The displayed reading is supposed to take in to account the above mentioned factors.