The raising and lowering of the weight can change the length of the pendulum.
By raising the weight up, the length of the pendulum is decreased and by lowering the weight down, the length of the pendulum is increased.
The time period of periodic motion of the pendulum ( or time taken to complete one oscillation) is directly proportional to the length of the pendulum.
As the Grandfather's clock is running slowly, thus, it is taking more time to complete the oscillation.
To decrease the time or to run the clock faster, the length of the pendulum should be decreased which can be done by raising the weight.
Thus, by raising the weight, the clock can start running at the normal time.