Speed tape calculations do not require weight
The speed tape indications for stall warning speeds are AOA based. Neither weight nor CG data is required. By comparing current AOA with known stall AOA (which is a function of current flap/slat setting) the AOA margin to stall is computed. This is translated into a speed margin to stall that is then applied to current speed.
On Boeings the speed tape includes a lower amber band. The top of the amber band corresponds to a 1.3g margin to stall such that turns up to 40 deg bank angle can be performed provided speed is maintained at/above the top of this amber band. Below the amber band is the red and white barber pole. Stick shaker fires when current speed drops below the top of the barber pole.
To repeat, all of these calculations are based on determining the margin from current speed to critical speeds based on the margin between current AOA and stall AOA. No knowledge of weight or CG is required.