  Using simple modules over the derivation Lie algebra $C[t]\frac{d}{d t}$ of
the associative polynomial algebra $C[t]$, we construct new weight Virasoro
modules with all weight spaces infinite dimensional. We determine necessary and
sufficient conditions for these new weight Virasoro modules to be simple, and
determine necessary and sufficient conditions for two such weight Virasoro
modules to be isomorphic. If such a weight Virasoro module is not simple, we
obtain all its submodules. In particular, we completely determine the
simplicity and the isomorphism classes of the weight modules defined in [C.
Conley, C. Martin; A family of irreducible representations of the Witt Lie
algebra with infinite-dimensional weight spaces. Compos. Math., 128(2),
153-175(2001)] which are a small portion of the modules constructed in this
paper.
