  We prove sharp weak type weighted estimates for a class of sparse operators
that includes majorants of standard $\alpha$-fractional singular integrals,
fractional integral operators, Marcinkiewicz integral operators, and square
functions. These bounds are knows to be sharp in many cases, and our main new
result is the optimal bound
$$[w]_{A_{p,q}}^{\frac{1}{q}}[w^{q}]_{A_{\infty}}^{\frac{1}{2}-\frac{1}{p}}\lesssim[w]_{A_{p,q}}^{\frac{1}{2}-\frac{\alpha}{d}}$$
for proper conditions which satisfy that three index $p$, $q$ and $\alpha$
ensure weak type norm of fractional square functions on $L^{q}(w^{q})$ with
$p>2$.
