This article presents progressively censored variable sampling plans for the Weibull distribution. Approximate maximum likelihood estimators are developed for estimating the parameters of interest. In the construction of sampling plans, asymptotic distribution theory is used to determine the sample size and the acceptance constant. Sampling plans are tabulated for selected progressive censoring patterns and specifications, for demonstration and comparison. A Monte Carlo experiment, conducted to investigate the accuracy of the asymptotic normal approximation, has shown that the procedure is sufficiently accurate for practical purposes. An example, based on data reported by Montanari and Cacciari from progressively censored aging tests on XLPE-insulated cable models, is given for illustration.