Vegetable grafting is increasingly recognized as an effective and sustainable plant production alternative. Grafted plants usually show increased uptake of water and minerals compared with self-rooted plants, mostly thought a consequence of the vigorous rootstocks selected. However, while studies frequently addressed the effects of rootstocks on the performance of scions, knowledge on the influences of scions on biomass allocation, morphology, and metabolic activity of roots is rare. In particular, the plasticity of root traits affecting resource acquisition and its efficiency remains poorly understood. Two different rootstock species, Cucurbita maxima × Cucurbita moschata and Lagenaria siceraria, were grafted in combination with melon (Cucumis melo) and watermelon (Citrullus lanatus). Self-grafted rootstocks were used as control. Plant biomass and root traits were determined after destructive harvesting 30 and/or 60 days after grafting. Traits included biomass allocation, leaf and root morphology, potential activities of four extracellular enzymes on root tips and basal root segments, and root respiration. Successfully grafted scions increase the ratio of root to whole plant dry matter (RMF), and increased ratios of root length to whole plant dry matter (RLR) and to plant leaf area (RL : LA). In contrast, morphological root traits such as diameter, tissue density, and specific root length remain surprisingly stable, and thus scion-induced changes of those traits may only play a minor role for the beneficial effects of grafting in Cucurbitaceae. Incompatibility in melon/L. siceraria grafts, however, was likely responsible for the reduced root growth in combination with clear changes in root morphological traits. Reduced root respiration rates seem to be the effects of a non-compatible rootstock–scion combination rather than an active, C-efficiency increasing acclimation. In contrast, heterografts with melon and watermelon frequently resulted in root-stock-specific, often enhanced potential enzymatic activities of acid phosphatase, β-glucosidase, leucine-amino-peptidase, and N-acetyl-glucosaminidase both at root tips and basal parts of lateral roots—presenting a potential and complementary mechanism of grafted plants to enhance nutrient foraging. The studied melon and watermelon scions may thus increase the nutrient foraging capacity of grafted plants by fostering the relative allocation of C to the root system, and enhancing the extracellular enzymatic activities governed by roots or their rhizobiome.