We have investigated optomechanical coupling in $n$-GaAs/$i$-GaAs bilayer cantilevers induced by optical band-gap excitation. The strain-assisted optopiezoelectric effect, which is associated with the separation of electron-hole pairs due to the built-in electric field, causes a time-delayed backaction force and influences the thermal vibration of the cantilevers. Vibration of the [110]-oriented cantilever is amplified by this optopiezoelectric backaction and the self-oscillation is induced for the strong excitation. In contrast, for the [$\overline{1}$10]-oriented cantilever, the optopiezoelectric backaction deamplifies the vibration because the direction of the piezoelectric stress is reversed. We have experimentally extracted the response time of this optopiezoelectric backaction, where the delay is on the order of the nonradiative recombination lifetime in GaAs. This optopiezoelectric backaction is maximized when the laser wavelength matches the optical absorption edge. This is because the strain-induced change in the optical absorption is maximized at the absorption edge and therefore a large force gradient results.