Proof for ACYCLIC PARTITION being NP-complete
In the current formulation, your problem can be proved to be NP-complete by a direct reduction from PARTITION.

Given $n$ positive integers, $S = \{a_1,a_2,...,a_n\}$ the PARTITION problem asks to find two disjoint subsets $S_1 \cup S_2 = S$ such that $\sum_{i\in S_1} a_i = \sum_{j \in S_2} a_j$.

So, just pick: $G = \{ V, \emptyset \}$ with $|V| = n$, set $m = 2$ and assign weight $a_i$ to node $u_i$ for all $i = 1,...,n$; set $B = \frac{1}{2} \sum a_i$, and set $K=0$ (arc costs and the acyclic constraints are irrelevant).

NOTE: my old answer was related to a different ACYCLIC PARTITION problem, and you can find it in the edits history below.