Information-theory procedures are powerful tools for multimodel inference and are now standard methods in ecology. When performing model averaging on a given set of models, the importance of a predictor variable is commonly estimated by summing the weights of models where the variable appears, the so-called sum of weights (SW). However, SWs have received little methodological attention and are frequently misinterpreted. We assessed the reliability of SW by performing model selection and averaging on simulated data sets including variables strongly and weakly correlated to the response variable and a variable unrelated to the response. Our aim was to investigate how useful SWs are to inform about the relative importance of predictor variables. SW can take a wide range of possible values, even for predictor variables unrelated to the response. As a consequence, SW with intermediate values cannot be confidently interpreted as denoting importance for the considered predictor variable. Increasing sample size using an alternative information criterion for model selection or using only a subset of candidate models for model averaging did not qualitatively change our results: a variable of a given effect size can take a wide range of SW values. Contrary to what is assumed in many ecological studies, it seems hazardous to define a threshold for SW above which a variable is considered as having a statistical effect on the response and SW is not a measure of effect size. Although we did not consider every possible condition of analysis, it is likely that in most situations, SW is a poor estimate of variable's importance.