  We prove new sharp asymptotic for counting the semistable elliptic curves
with two marked Weierstrass points at $\infty$ and $0$ and also the cases where
$0$ is a 2-torsion or a 3-torsion marked Weierstrass point over
$\mathbb{F}_q(t)$ by the bounded height of discriminant $\Delta(X)$. We
consider the motivic probabilities over any basefield $K$ with $\text{char}(K)
\neq 2,3$ of picking a nonsingular semistable elliptic surface over
$\mathbb{P}^{1}$ with two marked Weierstrass sections at $\infty$ and $0$ such
that marked Weierstrass section at $0$ is 2-torsion or 3-torsion. In the end,
we formulate an analogous heuristics on $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$
for the ratio of the semistable elliptic curves with a marked rational
2-torsion or 3-torsion Weierstrass point at $0$ out of all semistable elliptic
curves with a marked rational Weierstrass points at $0$ over $\mathbb{Q}$ by
the bounded height of discriminant $\Delta$ through the global fields analogy.
