Mast rake will affect the helm balance to a large extent. Raking a mast aft usually increases weather helm and raking forward has the opposite effect. If it is slightly raked aft then I would take this out and see how the helm feels. It is very important to make sure that the mast stays "in chord" eg. Straight up and down. Sight up the sail track, to check this.
If this does not make a substantial difference then have a look at your mainsail set as it could well be that it is "too full" in 15 knots of wind. Correct this by increasing out haul tension and halyard tension, and pull down on your boom kicking tackle. (This runs between the base of the mast to a point 1/3 the way out the boom from the gooseneck and I am assuming you have one of these fitted.) This flattens the sail and moves the centre of effort forward.
If the mainsail is old is becoming "too full" it will induce more & more weather helm when hard on the wind. The solution is to have it recut.
The other point to note is that when you bear the bow off the wind and ease the sails you will find that this will also increase weather helm due to the centre of effort being moved out board. To correct this try easing out the mainsail by letting the boom move down to leeward on the mainsheet traveler or by easing the mainsheet.
I can balance our boat so that she sails herself however this can only be achieved after setting her up for the prevailing conditions.