  We prove equidistribution of Weierstrass points on Berkovich curves.
  Let $X$ be a smooth proper curve of positive genus over a complete
algebraically closed non-Archimedean field $K$ of equal characteristic zero
with a non-trivial valuation.
  Let $L$ be a line bundle of positive degree on $X$. The Weierstrass points of
powers of $L$ are equidistributed according to the Zhang-Arakelov measure on
the analytification $X^{an}$. This provides a non-Archimedean analogue of a
theorem of Mumford and Neeman.
  Along the way we provide a description of the reduction of Weierstrass
points, answering a question of Eisenbud and Harris.
