Various criteria of broadband beamformer design for microphone arrays have been proposed in the literature. However, weighting functions used in these criteria are usually fixed as some constants. Instead, this paper fully exploits the degrees of freedom in weighting functions to design broadband beamformers by using the variably-weighted least squares method. By doing so, we demonstrate that efficient and flexible broadband beamforming can be achieved with passband shaping characteristics while keeping a minimal stopband level. Several design examples are presented to demonstrate the performance of the proposed algorithm.