  We study the density of rational points on a higher-dimensional orbifold
$(\mathbb{P}^{n-1},D)$ when $D$ is a $\mathbb{Q}$-divisor involving
hyperplanes. This allows us to address a question of Tanimoto about whether the
set of rational points on such an orbifold constitutes a thin set. Our approach
relies on the Hardy-Littlewood circle method to first study an asymptotic
version of Waring's problem for mixed powers. In doing so we make crucial use
of the recent resolution of the main conjecture in Vinogradov's mean value
theorem, due to Bourgain-Demeter-Guth and Wooley.
