What causes you to not exert your full weight despite making contact with the elevator floor?
This winds up being a slightly complicated interaction with four things to keep track of. First there is gravity, second there is the normal contact force with the floor which can be modeled as a very stiff elastic spring, third the acceleration of the elevator, and fourth your acceleration.
Now, gravity is a fixed force, and the mechanism of the elevator is constructed to deliver a safe acceleration regardless of the load as long as it is within the designed limits. So you can think of the acceleration of the elevator as being fixed also. So the only variable things are the elastic force and your acceleration.
If your acceleration exceeds the elevator’s acceleration then the floor will compress and the elastic force will increase. As the floor is represented as a very stiff spring the force increases very sharply with a very small compression. The sharply increased elastic force correspondingly reduces your acceleration until it matches that of the elevator.
If your acceleration is less than the elevator’s acceleration then the reverse happens. The sharply reduced elastic force increases your acceleration until it again matches that of the elevator.
Either way the floor deforms enough so that the normal force between you and the elevator is the exact value necessary so that your acceleration matches the elevator’s acceleration.