  Let $S$ be an infinite-type surface and $p\in S$. We show that the
Thurston-Veech construction for pseudo-Anosov elements, adapted for
infinite-type surfaces, produces infinitely many loxodromic elements for the
action of $Mod(S;p)$ on the loop graph $L(S;p)$ that do not leave any
finite-type subsurface $S'\subset S$ invariant. Moreover, in the language of
Bavard-Walker, Thurston-Veech's construction produces loxodromic elements of
any weight. As a consequence of Bavard and Walker's work, any subgroup of
$Mod(S;p)$ containing two "Thurston-Veech loxodromics" of different weight has
an infinite-dimensional space of non-trivial quasimorphisms.
