  Recently, perovskite related BaPbO$_3$ has attracted attention due to its
hidden topological properties and, moreover, has been used as a thin layer in
heterostructures to induce two-dimensional superconductivity. Here we
investigate the normal state electronic transport properties of thin films of
BaPbO$_3$. Temperature and magnetic field dependent sheet resistances are
strongly affected by two-dimensional quantum effects. Our analysis decodes the
interplay of spin--orbit coupling, disorder, and electron--electron interaction
in this compound. Similar to recently discussed topological materials, we find
that weak antilocalization is the dominant protagonist in magnetotransport,
whereas electron--electron interactions play a pronounced role in the
temperature dependence. A systematic understanding of these quantum effects is
essential to allow for an accurate control of properties not only of thin films
of BaPbO$_3$, but also of topological heterostructures.
