This study examines the behavior of a thin liquid film flowing on an inclined plane subject to imposed shear stress. The liquid’s time-reversal symmetry is broken, and we consider the odd part of the viscosity to describe the Navier–Stokes equation. To investigate the interplay between the imposed shear and odd viscosity on the flow dynamics, we develop a weighted residual model (WRM). We determine the model’s critical Reynolds number (Rec) through linear stability analysis. Our findings indicate that uphill shear tends to stabilize the flow, while downhill shear enhances the instability, albeit reduced by the presence of odd viscosity. We also construct an Orr–Sommerfeld (OS) type eigenvalue problem for normal mode analysis and derive Rec. We discover that in the longwave regime, RecWRM=RecOS. Finally, our numerical simulations of the model align well with our linear stability analysis.