Doubly robust estimators have long been advocated in the literature on missing data and causal inference. Recently, their use has also been proposed for inference in non-probability sampling. As in the missing data setting, non-probability sampling introduces a selection bias problem. Consequently, making valid inferences requires the use of auxiliary variables and modeling their influence on either the outcome variable or the selection mechanism. A doubly robust estimator requires specifying both a model for the selection mechanism and a model for the outcome variable, ensuring consistency if either model is correctly specified. This study aims to analyze how the performance of certain doubly robust estimators is affected when the selection mechanism is misspecified, particularly when it generates extreme and highly variable weights. The findings emphasize the importance of evaluating the empirical distribution of estimated weights, even when using a doubly robust estimator.