Angle-Dependent Weighted MUSIC or Weighted Norm MUSIC is a broad class of MUSIC-like parameter estimators which includes as special case the standard `spectral' MUSIC. Based on a general approach for deriving the point statistics of the signal-subspace estimators, the relation between the large-sample moments of MUSIC and Angle-Dependent Weighted MUSIC is presented in this paper. The optimum weight function resulting in the estimator with zero bias of order N-1 is derived. The approximate realizations of this optimum estimator in a parametric subclass of Angle-Dependent Weighted MUSIC for arrays measuring closely spaced sources are discussed. Simulation examples verify the theoretical analysis and demonstrate the proposed estimators have small estimation biases over a wide range of signal-to-noise ratio.