We investigated—both experimentally and numerically—the operation of a weakly birefringent cavity fiber laser under different net cavity dispersion values. Experimentally, we found that under coherent cross-polarization coupling, either in-phase or anti-phase low frequency intensity modulations between the two orthogonal polarization components of the laser emission could be obtained. The evolution of the periodic intensity modulations in the fiber laser under different operation conditions was studied. In this paper, we show that under suitable conditions, they can be shaped into a train of bright-bright, dark-dark, or dark-bright vector solitons.