A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after another. The order in which these algorithm select the variables potentially have significant impact on the search performance. Various heuristics have been proposed for choosing good variable ordering. Many powerful variable ordering heuristics weigh the constraints first and then utilize the weights for selecting good order of the variables. Constraint weighting are basically employed to identify global bottlenecks in a CSP. In this paper, we propose a new approach for learning weights for the constraints using competitive coevolutionary Genetic Algorithm (GA). Weights learned by the coevolutionary GA later help to make better choices for the first few variables in a search. In the competitive coevolutionary GA, constraints and candidate solutions for a CSP evolve together through an inverse fitness interaction process. We have conducted experiments on several random, quasi-random and patterned instances to measure the efficiency of the proposed approach. The results and analysis show that the proposed approach is good at learning weights to distinguish the hard constraints for quasi-random instances and forced satisfiable random instances generated with the Model RB. For other type of instances, RNDI still seems to be the best approach as our experiments show.