The paper presents analysis of the methodology of "weighing" as specific approach of finding a decision by the court in the situation, where the competition of human rights takes place. In the first part of the paper authors examine human rights as an object of "weighing" and demonstrates difficulties, arising within jurisdictional defense of competing rights, as well as the reasons of such difficulties. The key to the following analysis of the issue is to consider human rights as legal principles and to consider any legal principles as norms of high degree of generality. Authors critically analyze current theories of legal principles, in particular, the widespread opposition of principles and rules as two qualitatively different phenomena. Competition of human rights is subsumed under general concept of competition (conflict, collision) of norms, this allows to apply the methods of H.Kelsen's general theory of norms. Considering the methodology of "weighing" of legal principles, proposed by R.Alexy, and its critical discussion in academic literature, authors come to the conclusion that R.Alexy's theory fails to achieve the aim of constructing the method of making decisions in the situation of contradictions between principles. Alternatively to the method of "weighing", authors propose to resolve situations of the competition of human rights by special rules of interpretation, the aim of which is to remove the contradiction. In the last part of the paper theoretical conclusions of authors are proved by the brief analysis of argumentation in concrete decisions of courts.