Search-optimization problems are plentiful in scientific and engineering domains. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall  integer linear programming, MaxSAT, optimization satisfiability modulo theory, (constraint) answer set programming. These paradigms vary significantly in their languages in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so called extended weight systems that eliminates syntactic distinctions between paradigms and allows us to see essential similarities and differences between optimization statements provided by paradigms.