Cellularity for weighted KLRW algebras of types B$B$, A(2)$A^{(2)}$, D(2)$D^{(2)}$

This paper constructs homogeneous affine sandwich cellular bases of weighted KLRW algebras in types $B$, $A^{(2)}$, $D^{(2)}$. Our construction immediately gives for the finite dimensional quotients these algebras. Since generalize KLR algebras, we also obtain and cellularity results (infinite dimensional)