I've never seen a "weeping" willow in bonsai. The thinnest branches are those which seem to winter-kill the most regularly. Outside of that, the branches only "weep" as the result of getting long enough for the weight of the ends to droop because of the length. That length is never obtained in a bonsai-sized tree. Someone, a better man than me, may show an example of a "weeping" willow in a bonsai-sized tree.
To manage what the OP has, trim to some kind of dome that pleases the eye, then defoliate by cutting all the leaves off at the petiole. Then, as continuing care trim any twig back to a bud below the canopy any twig that threatens to grow beyond the imaginary dome of the canopy. Defoliate whenever the tree grows too dense. Be prepared to defoliate every 6 weeks.