  Many recent results in combinatorics concern the relationship between the
size of a set and the number of distances determined by pairs of points in the
set. One extension of this question considers configurations within the set
with a specified pattern of distances. In this paper, we use graph-theoretic
methods to prove that a sufficiently large set $E$ must contain at least
$C_G|E|$ distinct copies of any given weighted tree $G$, where $C_G$ is a
constant depending only on the graph $G$.
