Bemrose et al. introduced weaving frames and later, Deepshikha et al. generalized them to weaving $K$-frames. In this note, as a generalization of these notions, we introduce approximate $K$-duals and investigate the properties of $K$-$g$-frames and weaving $K$-$g$-frames. We show that woven $K$-$g$-frames and weakly woven $K$-$g$-frames coincide. We also study perturbation and erasure of woven $K$-$g$-frames and we show that they are stable under small perturbations. Also we generalize some of the known results in frame theory to $K$-$g$-frames and weaving $K$-$g$-frames.