For parameters $n,δ,B,C$, we obtained a sharp asymptotic formula for the number of $(n+\lfloor n^δ\rfloor)^2$-dimensional binary contingency tables with non-uniform margins taking values of $\lfloor BCn\rfloor$ and $\lfloor Cn\rfloor$. Furthermore, we compared our sharp asymptotics with the classical independence heuristic estimate and proved that the independence heuristic overestimates by a factor of $e^{Θ(n^{2δ})}$. Our comparison is based on the analysis of the correlation ratio and an explicit bound for the constant in $Θ$ is also obtained.