The overly light action could be caused by one or more or considering the age of the piano probably all of the following items.
1. Hammers have become too light due to repeated filing and shaping and it's time to dump them.
2. Worn out key bushings.
3. Worn out pinning in the action centers.
4. Dammit there was a fourth item that was in my mind a minute ago but now it's disappeared. A sign that I'm getting old and senile.
At any rate you need a competent tech to evaluate your action. You could be in for anything from $500 to $5000 depending on how thoroughly you want to go into this. Chances are you have a lot of old worn out parts in the action and to do the job in the most thorough manner in order to return the action to the state it was in when new is going to mean replacing lots of parts and involve lots of labor and will be a $4000 to $5000 project.
It's a lot like when the engine in your car is showing serious signs of age and wear and your mechanic says he can do a ring and valve job and keep things going fairly well for a while longer for a medium cost, or he can tear the whole engine down bottom to top and do a complete overhaul and you will have essentially a new engine but it will cost you a bundle more, or you can just take the cheap route and throw a can of STP in every so often and keep limping along. Or you can just dump the thing.
Piano rebuilder, Pasadena, CA www.pianosource.com