  The notion of weighted $(b,c)$-inverse of an element in rings were
introduced, very recently [Comm. Algebra, 48 (4) (2020): 1423-1438]. In this
paper, we further elaborate on this theory by establishing a few
characterizations of this inverse and their relationships with other $(v,
w)$-weighted $(b,c)$-inverses. We introduce some necessary and sufficient
conditions for the existence of the hybrid $(v, w)$-weighted $(b,c)$-inverse
and annihilator $(v, w)$-weighted $(b,c)$-inverse of elements in rings. In
addition to this, we explore a few sufficient conditions for the reverse-order
law of the annihilator $(v, w)$-weighted $(b,c)$-inverses.
