  The purpose of this article is twofold: to prove a pointwise equidistribution
theorem with an error rate for almost smooth functions, which strengthens the
main result of Kleinbock, Shi and Weiss (2017); and to obtain a
L\'evy-Khintchin theorem for weighted best approximations, which extends the
main theorem of Cheung and Chevallier (2019).
  To do so, we employ techniques from homogeneous dynamics and the methods
developed in the work of Cheung-Chevallier (2019) and Shapira-Weiss (2022).
