Algorithm

$1.$ Compute tin[v] and tout[v] via DFS.

$2.$ Build array where arr[tin[v]] = +value[v] and arr[tout[v]] = -value[v].

$3.$ Use BIT or segment tree for prefix sums with point updates.

$4.$ For path sum query to $v$: query prefix sum from $0$ to tin[v].

$5.$ For value update on $v$: update arr[tin[v]] and arr[tout[v]] with the delta. Each query is $O(\log n)$.

Space complexity is $O(n)$ for the data structures used.