  We prove pointwise equidistribution with an error rate of each $H$-orbit in
$SL(d,\mathbf{K})/SL(d,\mathbf{Z})$ for a certain proper subgroup $H$ of
horospherical group over a function field $\mathbf{K}$, extending a work of
Kleinbock-Shi-Weiss. Moreover, we obtain an asymptotic formula for the number
of integral solutions to the Diophantine inequalities with weights,
generalizing a result of Dodson-Kristensen-Levesley. This result enables us to
show pointwise equidistribution for unbounded functions of class $C_\alpha$,
which was first introduced by Eskin-Margulis-Mozes.
