The population value of coefficients of correlation based on ranks depends only on the copula underlying the true distribution. We consider data sets that share the same dependence structure, but present different margins. For instance, data may be expressed in different currencies or measured by indices that cannot be compared across populations. A mixture of empirical copulas is built, yielding weighted coefficients of correlation. The consistency of the estimates and their asymptotic distributions are derived for scalar weights. We also consider the case where data-based weights detect adaptively the similarities between the copulas underlying each population, with the idea of making a compromise between bias and variance. Simulations are used to explore the finite sample behavior of these weighted methods.