An iterative adaptive weighted filtered backprojection (FBP) approach was applied to our photoacoustic imaging (PAI) of the optical absorption in biological tissues from limited-view data. By using an image-based adaptive weighted PAI reconstruction, we can modify the defect of the artifacts degrading the quality of the image. Results of numerical simulations demonstrated that the proposed algorithm was superior to FBP in terms of both accuracy and robustness to noise. Reconstructed images of biological tissues agreed well with the structures of the samples. The resolution of the PAI system with the proposed method was experimentally demonstrated to be better than 0.14 mm. By using the proposed method, the imaging quality of the PAI system can be improved.