Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modelings search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall MaxSAT or  answer set programming. These paradigms vary significantly in their languages and in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so called weight systems that eliminates syntactic distinctions between paradigms and allows us to see essential similarities and differences between optimization statements provided by paradigms. This unifying outlook has a significant simplifying and explanatory potential in the studies of optimization and modularity in automated reasoning and knowledge representation providing technical means for bridging distinct formalisms and developing translational solvers.