  Weak coloring numbers generalize the notion of degeneracy of a graph. They
were introduced by Kierstead \& Yang in the context of games on graphs.
Recently, several connections have been uncovered between weak coloring numbers
and various parameters studied in graph minor theory and its generalizations.
In this note, we show that for every fixed $k\geq1$, the maximum $r$-th weak
coloring number of a graph with simple treewidth $k$ is $\Theta(r^{k-1}\log
r)$. As a corollary, we improve the lower bound on the maximum $r$-th weak
coloring number of planar graphs from $\Omega(r^2)$ to $\Omega(r^2\log r)$, and
we obtain a tight bound of $\Theta(r\log r)$ for outerplanar graphs.
