We show that every weighted quasi-metric space can
be identified with a subspace of a space of some canonical type,
which is constructed from a metric space.
We also present a very simple method to construct a weighted
quasi-metric space, as the graph of a function defined on a metric
space, and show that every weighted quasi-metric space arises in
this way.
Similar results may be obtained if we drop the requirement that
the weight function have nonnegative values.
