The symmetry of polarization distribution pattern about the solar meridian is an important cue for underwater polarization navigation. However, the waves lead to the distortion and fragmentation of the optical refraction surface. It gives rise to a challenge of extracting the solar meridian of disturbed polarization images. A dual-weight iterative weighted least squares method is proposed to address the problem. This algorithm enhances the accuracy of solar meridian extraction through a comprehensive design of dual weights. One of weights integrates data dispersion to account for variability in the measurements. Another incorporates confidence levels of the polarization angle to refine the weighting strategy. By iteratively optimizing these weights, the algorithm effectively improves the precision of the solar meridian extraction. Simulation and sea trial results show this algorithm has the advantages of high accuracy and low time consumption that current researches suffered. This research enables precise orientation and pathfinding in wavy underwater environments.