We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames can be used as reference. Our goal is to use the reference signal to reduce the number of required measurements for reconstruction. We achieve this via a reweighted ℓ1-ℓ1 minimization scheme that updates its weights based on a sample complexity bound. The scheme is simple, intuitive and, as our experiments show, outperforms prior algorithms, including reweighted ℓ1 minimization, ℓ1-ℓ1 minimization, and modified CS.