For Gaussian sampling matrices, we provide bounds on the minimal number of measurements required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the true underlying support. Our main contribution is that for a sparse vector supported on an unknown set with , if has weighted cardinality , and if the weights on exhibit mild growth, for and , then the sample complexity for sparse recovery via weighted -minimization using weights is linear in the weighted sparsity level, and . This main result is a generalization of special cases including a) the standard sparse recovery setting where all weights , and ; b) the setting where the support is known a priori, and ; and c) the setting of sparse recovery with prior information, and depends on how well the weights are aligned with the support set . We further extend the results in case c) to the setting of additive noise. Our results are nonuniform that is they apply for a fixed support, unknown a priori, and the weights on do not all have to be smaller than the weights on for our recovery results to hold.