  We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted
hypersurface of index $1$ is greater than or equal to $1/2$. Combining this
with the result of Stibitz and Zhuang \cite{SZ19} on a relation between
birational superrigidity and K-stability, we prove the K-stability of a
birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of
index $1$.
