This is probably not what you're looking for, but in classical economics a violation of Pareto efficiency could be considered a form of moral imbalance. (Pareto efficiency itself can also lead to constellations we consider immoral, though.) Then there are also theories of fair resource allocation in which people try to find principles for balancing resources in a fair way. For example a transfer that takes away an amount a of goods from a rich and gives this a to a poor and afterwards still leaves the rich at least as wealthy as the poor is called a Pigou-Dalton transfer. There are many similar principles and many interesting impossibility theorems in this area. For example, you cannot have social welfare based on Pigou-Dalton transfers that always remains Pareto efficient. Unfortunately the math behind this is not very easy.
Of course, this tradition is mostly utilitarian and usually concerned with goods, commodities, and welfare in the sense of 'utility', not with moral values. However, a mathematically sound theory of moral balance would have to use very similar methods and face similar problems as this research in welfare economics and social choice. Some people work on this connection, e.g. Vlodek Rabinowicz in Sweden.