That's exactly my question.
The computers calculate that.
Lift = 0.5 rho V^2 S Cl
You can disregard the 0.5 for this. rho (density) can be calculated using static pressure and total air temp probes, you'd need a humidity measurement to get precise figures of density. V^2 is your TAS squared. S is the surface area of the lifting surface which can be stored in the computer. Cl would be related to your angle of attack in a certain configuration. That graph would change quite a bit and there are calculations/transformations for all changes. If you read the article by Boeing I just posted here it'll explain quite a bit. The Cl vs AoA graph would change depending on a number of variables that is explained more in the Boeing article.
The total lift at 1G will = the total weight. By calculating what the total lift is (including the lift on the horizontal stabilizer), they can know what the total weight of the aircraft is. They could even calculate the Center of Gravity! Knowing all this for 1G, they could apply transformations that would calculate the weight of the plane when it's not at 1G.
All of this stuff is easy to calculate. But does your airplane have the capability? - I don't know. I'm not intimately familiar with Boeing or Airbus systems on each aircraft so I don't know what their capability is.