a weight attached the end of of the string to tension the string ???

That keeps the string at constant tension, but if the temperature changes, or if a change in humidity changes the length of the guitar, you'd have to have something to tune the weights (????)

My suggestion would be to dispense with the mechanics and just run an electric current lengthwise down each string. The current can be controlled to warm the string just to the extent needed to drop the pitch to the correct point, assuming that each string is tuned just a little sharp before turning on the juice.

And I can get you a great deal on asbestos gloves, if quantities ordered are sufficient.

John