Few-layer flakes of MoS₂ or MoSe₂ with lateral dimensions over 1 µm were grown on graphite using chemical vapor deposition, yielding layered samples MoS₂/graphite or MoSe₂/graphite, respectively. Next, an attractive van der Waals (vdW) force on a sharp AFM tip was measured from graphite, MoS₂/graphite and MoSe₂/graphite as a function of a separation between the tip and sample. The vdW force from the layered samples is significantly weaker than from graphite alone, suggesting screening of the semimetallic graphite by the semiconducting MoS₂ and MoSe₂. Statistical analysis over 6 different measurements indicates that the single-layer MoSe₂ screens 59 ± 14 % and the single-layer MoS₂ 71 ± 12 % of the force from graphite. The double-layer samples exhibit even stronger screening, with the double-layer MoSe₂ screening 77 ± 24 % and the double-layer MoS₂ 94 ± 8 %of the vdW force from graphite. The observed results demonstrate a possibility to engineer and control the nanoscale vdW forces in a bottom-up approach, and provide a critical experimental platform for testing the quantum electrodynamic Lifshitz theory of vdW interactions.