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

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces