Rupert Li's congruence conjecture for weighted hypersurfaces

Let $S=\mathbb{F}_q[x_0,\ldots,x_n]$ be graded by positive weights $w_i$, and let $X=V(F)\subseteq\mathbb{P}(w_0,\ldots,w_n)$ be defined by a nonzero weighted homogeneous polynomial $F\in S$ of degree $d\leq n$. Rupert Li's congruence conjecture. One has

$$|X(\mathbb{F}_q)|\equiv 1\pmod q.$$

This was suggested on the basis of computer research after a proved congruence modulo the characteristic prime. The source does not give a proof or a resolution of the stronger congruence modulo $q$.