It depends on the lockup type.

Reducing the arm weight on a 2-stage will not really change the timing, just the overall force it can generate. The arms on a 2-stage lockup will apply at the same time no matter how much or little weight is on the arms. Removing weight reduces the amount of overall clamping force the lockup can generate which may cure an aggressive condition on the bottom end but could also lead to it driving through the clutch on the top end.

On a multistage lockup altering the amount of weight on the arms will change the timing of the arms. The counterweight is what gives the arm the ability to override the spring, so reducing the weight will cause the lockup to apply a bit later in the run. Conversely, adding weight will cause the arm to apply a bit sooner in the run. This is why we recommend keeping the weight the same on all the arms of a multistage lockup. However, removing weight or adding weight also alters the way the arm applies all the way down the track. Adding weight will also make the arm much more aggressive throughout the RPM band. Removing weight lowers the arms ability to override the spring resulting in much reduced pressure at high RPM. In other words if you need to change the timing on the arms, do it with the springs, not the weight.

Mismatched weights on the arms of a multistage can lead to a tuning nightmare. Normally, the arms with the lower number springs come in first, the higher number springs come in second. If you sufficiently mismatch the weights you can cause the arms to swap positions when it comes to application.