The weighted exponential distribution is discussed in the literature as a generalization of the standard exponential distribution. This distribution is a better fit in many practical purposes as compared to the distributions like exponential, Weibull and gamma, even though the shape of the weighted exponential distribution is similar to the above said. If a product is designed to have high reliability and long lifetime, it is good to consider accelerated acceptance sampling plan for obtaining lifetime information quickly, and thereby one can significantly reduce the total cost of testing. In this article, we develop two acceptance sampling plans for weighted exponential distribution under constant stress accelerated condition using type II censored samples. First sampling scheme is designed using order statistics concept and the second is developed using asymptotic distribution of the model parameters. The plan parameters of the two plans are obtained by solving optimizations problems which minimize expected total testing costs. Several numerical examples are considered to illustrate our plans. Finally, a comparison study of resulting plans based on costs is carried out.