  Using $p$-adic local Langlands correspondence for
$\operatorname{GL}_2(\mathbb{Q}_p)$, we prove that the support of patched
modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin
meet every irreducible component of the potentially semistable deformation
ring. This gives a new proof of the Breuil-M\'ezard conjecture for
2-dimensional representations of the absolute Galois group of $\mathbb{Q}_p$
when $p > 2$, which is new in the case $p = 3$ and $\bar{r}$ a twist of an
extension of the trivial character by the mod p cyclotomic character. As a
consequence, a local restriction in the proof of Fontaine-Mazur conjecture by
Kisin is removed.
