We conducted a study on the variations of the fragment anisotropy parameters (β) along the Fano profiles for the predissociation of the D2 molecule. These variations, known as β profiles, were measured for the D(2l) fragments from the predissociation of the 4pπD′Πu1υ′=1 and 4pσB″Σu+1υ′=2 states. The measured β profiles show significant asymmetry and broader linewidths compared to the corresponding Fano profiles. By fitting the β profiles, we were able to determine the fragment anisotropy parameters associated with the resonance state, continuum state, and the interference effect between them. Additionally, we determined the ratios of the absorption cross sections between the unperturbed and perturbed continuum states interacting with the resonance states although these ratios were found to be very small. Furthermore, we derived approximate formulas to calculate the parameters characterizing the β profile. Despite the linewidths of the four Fano profiles being narrower than our instrumental resolution, we were still able to determine the product of the linewidth with the Fano q parameters. These findings demonstrate the utility of the β profile as an effective tool for studying the predissociation dynamics in diatomic molecules.