In this work, our objective is to heuristically discover a simplified form of functional dependencies between variables called weak dependencies. Once discovered, these relations are used to rank the variables. Our method shows that these relations can be detected with some acceptable overhead during constraint propagation. More precisely, each time a variable y gets instantiated as a result of the instantiation of x, a weak dependency (x,y) is recorded. As a consequence, the weight of x is raised, and the variable becomes more likely to be selected by the variable ordering heuristic. Experiments on a large set of problems show that on the average, the search trees are reduced by a factor 3 while runtime is decreased by 31% when compared against dom-wdeg, one of the best dynamic variable ordering heuristic.