How does it realize that you don't weigh 100T, and that it needs to show speeds for 110T?
Much of the basics are captured in other posts but the following may make things a tad simpler. As a sideline point, some of the ideas in a few posts are a bit wide of the mark but that's aviation - ask ten pilots a question and get twenty different answers ...
The basics are comparatively straightforward even if there is a lot of wind tunnel work and computer code cutting to make it work in the cockpit.
The underlying computer models built into the magic black boxes will know the relevant parameters which determine lift from onboard measuring systems - incidence (AoA), density, speed, and a reference area to balance up the units. In addition (and most folks either forget or are not aware of these) Reynolds Number and Mach Number affect the shape of the lift curve slope (incidence against lift coefficient) as well as incidence.
If we take the simple case of cruise flight, for instance, we can put
lift = weight = some constant x lift coefficent x speed squared
so, if we know the weight and the speed, then we can figure out what lift coefficent we should have for a given set of conditions. The result is that we know at what incidence the aeroplane should be flying for that lift coefficient.
If the calculated incidence is higher or lower than the real world incidence on the day, then the presumed weight is wrong. It follows that we can reverse the sums to figure out what the weight is.
Stall is proportional to the square root of weight so the magic box can figure the correct stall speed and adjust the presentation made to the pilot accordingly.
Why can't PPRuNe have a QUOTE button like every other forum?
If you look along the top line (starting with the bold symbol) you will find the
quote symbol.
Simpletons like me just highlight quoted material by italicising or similar.
Given that the critical AoA remains constant
A simplistic (if useful for basic pilot training) view. But be aware that Re and M come into the lift curve shape as well as incidence (AoA). To save my having to try and write a complicated equation, you might like to have a look at any of the web sources which cover this sort of stuff, such as
here.
The flight is not affected if we do not enter the weights.
.. because the boxes can figure out what the weight is to a reasonable accuracy.
You will stall the wing above AoA max regardless of your airspeed when you get there.
.. but be careful of some sideline issues. Published stall data usually is based on certification testing at low pitch rates. Things are a bit different at high rates - accelerated or g stalls. Indeed, at very high pitch rates, the stall angle can be pushed much higher due to the formation of spanwise vortex flows above the wing.