Imagine a rudder which pivots about its leading edge. To move it, against the water flow, requires your muscle applied through tiller or wheel.
Now imagine a rudder which pivoted along an axis halfway between its leading and trailing edges. You begin to initiate a turn by moving the helm slightly one way, let's say to port. Once waterflow hits the starboard face of the rudder, ahead of its pivot, water pressure will do almost all the work of turning the rudder the rest of the way - in fact you may have to restrain it from going too far. That's a balanced rudder - in fact in reality it's an over balanced rudder, because you've lost the feel that heps you judge how much helm to apply and when to begin to straighten up.
Rule of thumb is that pivoting a rudder anymore than about 25% of the way back from the leading edge is too much.
When going astern most rudders are drastically overbalanced, that is you use muscle power to stop the rudder turning rather than to make it turn.
You'd cure overbalance by moving the axis of pivot forward (very complicated), by reducing area in front of the pivot, or by adding area aft of it.
Rudder balance is a separate topic from weather or lee helm, which is caused by an imbalance between the centre of effort of the sails and the centre of lateral resistance of the hull.
Seems to make sense as my transom hung rudder is actually raked forwards, ie the bottom of the leading edge is in front of the top.
If I therefore remove some of the forward area of the rudder to improve the balance, will I be shifting the centre of lateral resistance forward or aft? If aft this will not help the lee-helm that my boat also suffers from!
I was hoping to rake the mast back more to cure the lee-helm, but I'm not sure I will be able to do it enough if I also remove the forward area of the rudder. I guess I can't win!
I had this problem once. Lost my rudder during the YM Triangle race 94 and had a new one built in Ireland. Despite sending the yard full plans from Van de Stadt, they ignored them and built a seriously overbalanced rudder. I sailed the boat back to England in that condition (in October) and let me tell you it was a horrible experience - the boat constantly oversteered and tried to pull the wheel out of my hands. The full story is on my website under "Initial Preparations - Triangle 94".
The only solution was to get the rudder completely rebuilt when I was back in England; this was done by Andrew Simpson, now the illustrious dep. ed. of PBO.
A friend had a similar problem on a transom hung rudder and helped solve the problem by placing a spacer behind the upper pivot point which made the rudder axis nearer to vertical. Maybe this could help in your case. In his case the transom sloped forwards .
Balance of the rudder and Weather / Lee Helm should not be so dependent on each other.
The Weather / Lee helm is a factor of the sails to hull relationship ... as another has already stated.
Rudder balance is a factor of the leading and trailing areas of the rudder blade .... as another also stated.
You should be able to reduce the leading area of the rudder blade, in your case slimming down the lower section till enough blade is left to assist in helming, but not so that it pulls the tiller over more than you want.
The weather / lee helm is sorted by raking / moving the mast, or by setting the sails differently.
Increasing foresail, decreasing main, moving mast forward, raking mast forward to reduce weather helm etc.
Opposite actions to reduce lee helm.
If you look at some of the older long keel boats, you will find that many have a slimmer bottom to the blade, if the blade area is large. Other ways were to have a slim blade running the whole length of the raked long keel edge.......
In your case the suggestion about a spacer is well advised and will indicate if it will work or not .... and a lot less expensive than a new rudder !