  We introduce and study a realistic model for superconductivity in twisted
bilayer WSe$_{2}$, where electron pairing arises from spin-valley fluctuations
in the weak-coupling regime. Our model comprises both the full continuum model
moir\'{e} bandstructure and a short-ranged repulsive interaction. By
calculating the spin-valley susceptibility, we identify a Fermi surface nesting
feature near half-filling of the top-most moir\'{e} band, which induces
significantly enhanced spin-valley fluctuations. We then analyze the dominant
Kohn-Luttinger pairing instabilities due to these spin-valley fluctuations and
show that the leading instability corresponds to a two-component order
parameter, which can give rise to nematic, chiral and topological
superconductivity. As our findings are asymptotically exact for small
interaction strengths, they provide a viable starting point for future studies
of superconductivity in twisted transition metal dichalcogenide bilayers.
