Hyperspectral unmixing (HSU) plays an important role in hyperspectral image (HSI) analysis. Recently, the HSU method based on sparse regression has drawn much attention. This paper presents a new weighted sparse regression problem for HSU and proposes two iterative reweighted algorithms for solving this problem, where the weights used for the next iteration are computed from the value of the current solution, and all the mixed pixels of an HSI are unmixed simultaneously. The proposed algorithms can be seen as the combinations of alternating direction method of multipliers and iterative reweighting procedure. Experimental results on both synthetic and real data demonstrate some advantages of the proposed algorithms over some other state-of-the-art sparse unmixing approaches.