Covariance-based detection is a low-complexity blind spectrum sensing scheme that exploits spatial and/or temporal correlations of primary signals. However, its performance severely degrades with the decrease of signal correlations. In this work, a weighted-covariance-based detector is proposed by introducing data-aided weights to the covariance matrix. The false alarm probability, decision threshold, and detection probability are analyzed in the low signal-to-noise ratio (SNR) regime, and their approximate analytical expressions are derived based on the central limit theorem. The analyses are verified through simulations. Experiments with simulated multiple-antenna signals and field measurement digital television signals show that the proposed weighted detection can significantly outperform the original covariance-based detection.