Since stall speed, and other speeds that depend on it, depends on weight, 'the computer' needs to 'know' the weight to calculate these speeds. For a specified configuration it is possible to calculate weight from AoA, airspeed, altitude and inertial data, but not from air data alone. Therefore the calculation is unlikely to be done in the ADC of 'your' airplane.
I figured that if all other parameters are known, weight can be roughly deduced. I remember reading that FBW Airbii would actually warn the pilot of a gross error in the FMGC weight.
However, my current plane (E145) has only a generic FMS with no performance database. The flight is not affected if we do not enter the weights.
Is it possible that the plane calculates the weight using the other known parameters, then uses the computed weight to put marks on the ASI?