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A novel data covariance model has recently been proposed for the subspace-based estimation of multiple real-valued sine wave frequencies. In this paper, we develop weighted subspace fitting approaches using this new data model. A new parameterization of the noise subspace is proposed. This parameterization is used to solve the subspace fitting problem analytically. An expression for the residual covariance matrix is derived. This covariance matrix is further used to obtain an optimally weighted Gauss-Markov estimator. A computationally efficient suboptimal weighting is also proposed, and the associated estimator is close to the Gauss-Markov estimator in performance. The suboptimal weighting strategy is quite general and can be used in other related applications. The performance of the algorithms are illustrated using numerical simulations. The proposed subspace fitting approach shows improved resolution performance. It is also robust to additive noise.