  In [Tame_quivers_and_affine_bases_I], we give a Ringel-Hall algebra approach
to the canonical bases in the symmetric affine cases. In this paper, we extend
the results to general symmetrizable affine cases by using Ringel-Hall algebras
of representations of a valued quiver. We obtain a bar-invariant basis
$\mathbf{B}'=\{C(\mathbf{c},t_\lambda)|(\mathbf{c},t_\lambda)\in\mathcal{G}^a\}$
in the generic composition algebra $\mathcal{C}^*$ and prove that
$\mathcal{B}'=\mathbf{B}'\sqcup(-\mathbf{B}')$ coincides with Lusztig's signed
canonical basis $\mathcal{B}$. Moreover, in type $\tilde{B}_n,\tilde{C}_n$,
$\mathbf{B}'$ is the canonical basis $\mathbf{B}$.
