Detecting single stuck-at faults more than once has been shown to be an effective way to achieve high defect coverage. Recently it was observed that the number of tests required to achieve n-detection of single-stuck-at faults using pseudo-random sources may increase as n.logn with increasing values of n. In this paper we investigate weighted pseudo-random BIST for n-detection of single stuck-at faults. We propose a hardware efficient weighted pseudo-random test pattern generator. Experimental results show that the proposed test pattern generator achieves n-detection of single stuck-at faults with test set sizes growing linearly with n. The hardware overhead grows modestly with n.