We explore photospheric emissions from stratified two-component jets, wherein a highly relativistic spine outflow is surrounded by a wider and less relativistic sheath outflow. Thermal photons are injected in regions of high optical depth and propagated until the photons escape at the photosphere. Because of the presence of shear in velocity (Lorentz factor) at the boundary of the spine and sheath region, a fraction of the injected photons are accelerated using a Fermi-like acceleration mechanism such that a high-energy power-law tail is formed in the resultant spectrum. We show, in particular, that if a velocity shear with a considerable variance in the bulk Lorentz factor is present, the high-energy part of observed gamma-ray bursts (GRBs) photon spectrum can be explained by this photon acceleration mechanism. We also show that the accelerated photons might also account for the origin of the extra-hard power-law component above the bump of the thermal-like peak seen in some peculiar bursts (e.g., GRB 090510, 090902B, 090926A). We demonstrate that time-integrated spectra can also reproduce the low-energy spectrum of GRBs consistently using a multi-temperature effect when time evolution of the outflow is considered. Last, we show that the empirical E _p-L _p relation can be explained by differences in the outflow properties of individual sources....