The effect of small changes in GaSb layer thickness on the photoresponse spectrum of InAs/GaSb superlattices (SLs) designed for mid-infrared detection was systematically investigated. The samples were grown by molecular beam epitaxy with precisely calibrated growth rates. The basic SL used for this study consisted of 40 periods of InAs (20.5 Å)/GaSb (X Å), where the nominal value for X was adjusted from 18 to 27 Å in four different samples. An InSb-like interface (IF) was inserted between the layers to balance the SL strain. By decreasing the GaSb width, the photoresponse cut-off wavelength (λc) was adjusted from 4.03 μm to 4.55 μm, i.e., the SL energy band gap is being decreased. This decrease in the energy separation between the first heavy hole band (HH1) and the first conduction band (C1) as the GaSb layer is narrowed is counter intuitive. However, this experimental trend can be explained by a modified envelope function approximation (EFA) calculation that includes the effect of in-plane asymmetry at InAs/GaSb interfaces. As expected, the HH band is pushed away from the top of the GaSb valence band as the GaSb layer width becomes narrower. However, at the same time the C1 band is significantly broadened by the increased wave function overlap of the electron states in the InAs layer. The trend to smaller band gap with narrower GaSb layers and other effects of the design changes on the photoresponse spectrum are discussed.