The inductive blockwise Alperin weight condition for $G_2(q)$ and ${}^3{D}_4(q)$

The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. We establish this condition for the groups $G_2(q)$, $q\ge 5$, and ${}^3{D}_4(q)$ for all primes dividing their order.