Although BOAC is obviously correct, I guess you want a bit more substance.
Windshear causes a change in airspeed due to the inertia of the aircraft. A change in airspeed influences the lift produced by the wing for the same angle of attack.
A lighter aircraft can "follow" the windshear more easily. In other words it can accelerate or decelerate quicker to adjust for the change in wind/relative airflow.