We propose a novel dynamic reweighted ℓ2 (DRℓ2) algorithm in the regime of dynamic compressive sensing. Our analysis shows that aiming to solve a Type II optimization problem, DRℓ2 is effectively minimizing a `convex-concave' penalty in the coefficients that transitions from a convex region to a concave function using knowledge of past estimations. DRℓ2 thus provides superior reconstruction performance compared with state-of-the-art dynamic CS algorithms.