We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions F_α for α < ω^ω, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses (F_α)^-1 or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest.