An extensive number of applications like rocket jet engines and gas turbines carry out atomization within a confined environment due to faster atomization ability and good mixing efficiency. Literature suggests that the effect of confinement on the breakup of droplets, liquid threads and annular jets is not elementary, but varies with liquid viscosity, surrounding medium viscosity and the confinement strength. The present weakly nonlinear temporal analysis unveils if a similar dynamic effect of confinement persists on the breakup of planar two-dimensional liquid sheets of varying viscosities. Moreover, to mimic air assist atomization, the surrounding gases are considered to flow with non-zero velocities. The study reveals that the presence of confinement at higher gas-to-liquid velocity ratios of 2.5 and 3 produces no apparent improvement in atomization at all liquid Reynolds number. However, at relatively low gas-to-liquid velocity ratios of 2 and 2.25, confinement leads to a faster breakup than an unconfined one. This effect is more pronounced at relatively low Reynolds number (Re<100). However, the overall influence of confinement on non-dimensional breakup time is weak as compared to its effect on the linear maximum growth rate; a counteracting effect of confinement on linear maximum growth rate and normalized second order disturbance amplitude is identified as the primary reason. The study also identifies the minimum confinement height (CH-1) for the liquid sheet to achieve breakup without touching the solid walls. Interestingly, maximum linear growth rate and minimum breakup time for a particular flow condition are always registered when confinement height equals CH-1.