In practice, the wrapped phase in interferometry is often affected by noise and discontinuity, and among the various types of phase unwrapping (PU) method, the weighted least-square (WLS) PU algorithm, as a global strategy, is widely utilized. However, the excessive smoothing effect exists within the process of PU. Therefore, it is necessary to conduct a comprehensively analysis of different WLS PU algorithms, which includes noise resistance, discontinuity characteristics, convergence speed, and accuracy. First, different weighting strategies were compared with detail for the WLS approach. Under slight noise condition, the edge detection map (EDM) and the filtering method both obtained relatively accurate and reliable phase information. However, when it comes to global multiplicative noise such as speckle noise, the filtering method showed better anti-noise performance than the EDM method, whereas EDM was more capable of dealing with discontinuous phase. Second, to improve the iterative convergence speed and accuracy, the initial value selection was analyzed in detail, and a new initial value selection method was proposed. Simulation and experiments were carried out and validated the results of the analysis.