  Let $F$ be a family of pseudo-disks in the plane, and $P$ be a finite subset
of $F$. Consider the hypergraph $H(P,F)$ whose vertices are the pseudo-disks in
$P$ and the edges are all subsets of $P$ of the form $\{D \in P \mid D \cap S
\neq \emptyset\}$, where $S$ is a pseudo-disk in $F$. We give an upper bound of
$O(nk^3)$ for the number of edges in $H(P,F)$ of cardinality at most $k$. This
generalizes a result of Buzaglo et al. (2013).
  As an application of our bound, we obtain an algorithm that computes a
constant-factor approximation to the smallest _weighted_ dominating set in a
collection of pseudo-disks in the plane, in expected polynomial time.
