Need a more nuanced approach to multiple testing? This paper presents a variety of methods for multiple hypotheses testing problems that incorporate weights, addressing the limitations of traditional approaches. It outlines various type-I error rates and possible formulations for both intersection and multiple hypotheses testing. An optimal per-family weighted error-rate controlling procedure is derived, and alternative approaches to family-wise error-rate control with weights are explored. These include both an alternative procedure for family-wise error-rate control and the control of a weighted family-wise error-rate. In particular, extensions and modifications of procedures based on Simes' test are discussed. These include a test of the overall intersection hypothesis with general weights and weighted sequentially rejective procedures for testing individual hypotheses. Furthermore, the false discovery rate controlling approach is extended to accommodate different weights, offering greater flexibility and control in multiple testing scenarios. This paper provides researchers with a comprehensive toolkit for conducting weighted multiple hypotheses tests.