Existence of path under weight and value budgets
Here is the idea of the reduction; I'll let you fill in the details.

We are given an instance of the partition problem, consisting of numbers $x_1,\ldots,x_n$ summing to $S$. We construct a (non-simple) graph on the vertex set $s = v_0,\ldots,v_n = t$. For $i=1,\ldots,n$, there are two edges from $v_{i-1}$ to $v_i$: one with weight $x_i$ and value $0$, and one with weight $0$ and value $x_i$. Our target weight and value are both $S/2$.

I'll let you figure out why this works, and convert it to a simple graph.