There is a prevalence of public interest over private interest because public interest is more important than private interest in maintaining a functioning society. Public interest is concerned with the well-being of society as a whole, while private interest is concerned with the well-being of individuals.
If a public norm violates an individual right, this problem can be resolved through the legal system. The legal system provides a framework for resolving disputes between individuals and the state, and for enforcing individual rights. If an individual believes that their rights have been violated by a public norm, they can challenge the norm in court. The court will then determine whether the norm is constitutional and whether it violates the individual's rights. If the norm is found to be unconstitutional, it will be struck down, and the individual's rights will be protected.