maintaining TreeSet sort as object changes value

As others have noted, there is no in-built way. But you can always subclass that TreeSet, with your constructor(s) of choice, and add in the required functionality:

public class UpdateableTreeSet<T extends Updateable> extends TreeSet<T> {

    // definition of updateable
    interface Updateable{ void update(Object value); }

    // constructors here
    ...

    // 'update' method; returns false if removal fails or duplicate after update
    public boolean update(T e, Object value) {
       if (remove(e)) {
           e.update(value);
           return add(e);
       } else { 
           return false;
       }
    }
}

From then on, you will have to call ((UpdateableTreeSet)mySet).update(anElement, aValue) to update the sorting value and the sorting itself. This does require you to implement an additional update() method in your data object.