As Runaway Gun said, if the weight increases, the lift also has to increase.
The lift formula is <Lift = 1/2 rho x Vsquared x wing area x CL>
Therefore if we keep the air density (rho) and the wing area the same, the only things we can adjust are the speed (V) and the angle of attack (which influences CL).
So if we need more lift due to increased weight we have to either increase the speed (V) or the angle of attack (CL).
Given that a particular wing will (nearly) always stall at the same angle of attack, the only way we can get more lift at that angle of attack is to increase the speed.