  We introduce the notion of an adelically summable normalized weight $g$,
which is a family of normalized weights on the Berkovich projective lines
satisfying a summability condition. We then establish an adelic
equidistribution of effective $k$-divisors on the projective line over the
separable closure $k_s$ in $\overline{k}$ of a product formula field $k$ having
small $g$-heights and small diagonals. This equidistribution result generalizes
Ye's for the Galois conjugacy classes of algebraic numbers with respect to
quasi-adelic measures.
