  Harron and Snowden counted the number of elliptic curves over $\mathbb{Q}$ up
to height $X$ with torsion group $G$ for each possible torsion group $G$ over
$\mathbb{Q}$. In this paper we generalize their result to all number fields and
all level structures $G$ such that the corresponding modular curve $X_G$ is a
weighted projective line $\mathbb{P}(w_0,w_1)$ and the morphism $X_G\to X(1)$
satisfies a certain condition. In particular, this includes all modular curves
$X_1(m,n)$ with coarse moduli space of genus $0$. We prove our results by
defining a size function on $\mathbb{P}(w_0,w_1)$ following unpublished work of
Deng, and working out how to count the number of points on
$\mathbb{P}(w_0,w_1)$ up to size $X$.
