  We prove that, for a $C^\infty$-generic contact form $\lambda$ adapted to a
given contact distribution on a closed three-manifold, there exists a sequence
of periodic Reeb orbits which is equidistributed with respect to $d\lambda$.
This is a quantitative refinement of the $C^\infty$-generic density theorem for
three-dimensional Reeb flows, which was previously proved by the author. The
proof is based on the volume theorem in embedded contact homology (ECH) by
Cristofaro-Gardiner, Hutchings, Ramos, and inspired by the argument of
Marques-Neves-Song, who proved a similar equidistribution result for minimal
hypersurfaces. We also discuss a question about generic behavior of periodic
Reeb orbits "representing" ECH homology classes, and give a partial affirmative
answer to a toy model version of this question which concerns boundaries of
star-shaped toric domains.
