  We study stochastic SQG equations on the torus $\mathbb{T}^2$ with
multiplicative transport noise in the $L^2$-setting. Under a suitable scaling
of the noise, we show that the solutions converge weakly to the unique solution
to the deterministic dissipative SQG equation. A similar scaling limit result
is proved also for the stochastic 2D inviscid critical Boussinesq equations.
