In this paper, we study the support recovery conditions of weighted ℓ₁ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from ℓ₁ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted ℓ₁ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted, ℓ₁ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.