Accurate estimation of query aspect weights is an important issue to improve the performance of explicit search result diversification algorithms. For the first time in the literature, we propose using post-retrieval query performance predictors (QPPs) to estimate, for each aspect, the retrieval effectiveness on the candidate document set, and leverage these estimations to set the aspect weights. In addition to utilizing well-known QPPs from the literature, we also introduce three new QPPs that are based on score distributions and hence, can be employed for online query processing in reallife search engines. Our exhaustive experiments reveal that using QPPs for aspect weighting improves almost all stateof-the-art diversification algorithms in comparison to using a uniform weight estimator. Furthermore, the proposed QPPs are comparable or superior to the existing predictors in the context of aspect weighting.