The period of a simple pendulum is given by the equation T=2*pi*sqrt(L/g) for small angles, that is a small swing from center. Notice that the period is affected by only 2 variables. L is the length of the pendulum and g is the force of gravity. In reality, there are other variables acting on our pendulum like air drag and the force used to drive the pendulum and keep it going. Without them, we would have a perpetual motion machine (which does not exist.) Since we cannot get away from these other variables, the simple pendulum equation provides only an estimate of the period. The more force that is put into the pendulum to drive it, more weight as it applies to this discussion, the farther we get from the simple pendulum equation. As long as this force is constant, ie, the weight is the same, the pendulum will maintain the same period. If the weight is changed, the length of the pendulum must be adjusted to compensate (changing the force of gravity is slightly more difficult.) This is the reason spring driven clocks speed up and slow down as the force from the spring changes as it unwinds.
Recall that the equation is only good for a small angle. To see the error caused by a large angle, check out this site.
If the pendulum is given a small swing, the theoretical period is very close to the experimental period. Give the pendulum a large swing and the difference between theoretical and experimental becomes much greater. Cool site!