Is it an $NP$-hard problem?
You're given an undirected graph $G(V,E)$ with vertex weight $w: V \to \mathbb{N}$ and a function $\mathrm{max}$-$\mathrm{visit}: V \to \mathbb{N}$ and a number $W$.
Does there exists a path in $G$ with total weight $W$ that does not visit any vertex $v$ more than $\mathrm{max}$-$\mathrm{visit}(v)$ times?