Hi Paul, if there is a lot of slack then that could be it.
I understand what you say about adding weight to a moving surface but if it is "mass balanced" it can only improve things.
As an example if you lose a wing from a model then as the wing comes down it rotates. If some weight is added to the leading edge it doesn't.
By adding weight to the leading edge of the rudder you are counteracting this tendency.
As a test take the linkage off the rudder and quickly move the body from left to right. The weight of the rudder makes it carry on when you stop the movement but if it's "mass balanced" it doesn't want to carry on.
If it is mass balanced to the point of being nose heavy then the leading edge of the rudder will want to carry on moving which has a damping effect instead of exagerating the problem.
You could always just tape some weight on and try it, if it doesn't work you can take it off easily.
Jim