Fast ion beta scaling of non-resonant modes (NRMs) with a safety factor profile close to but above unity ( 1) in tokamak plasmas with a reversed magnetic shear configuration, particularly those with a weak shear ( ~ 0) of around , are analysed in this study. It is found that, in three different regimes of magnetic shear configuration, the fast ion beta scaling of the NRM growth rate are: (1) in the small but finite regime, (2) , in the = 0 regime, and (3) in an almost flat q-profile regime. The scalings suggest that the growth rate of the mode is related to the fast ion beta and weakens as the q-profile is flattened. The dispersion relation of NRM in the = 0 regime is then derived and analysed.