The circulatory system is a closed loop (Figure 1.04), so what blood is "pumped up", falls back down again - much like a common siphon. Thus, the heart does no work against gravity in moving the blood.
Nevertheless, gravity does alter the pressures inside and outside of blood vessels. In the upraised arm, as when you are screwing a light bulb into a ceiling socket, gravity subtracts pressure from the blood vessels, decreasing transmural pressure. Thin-walled vessels such as venules collapse, which in turn increases vascular resistance. This impedes blood flow, producing localized ischemia and the pain and numbness we experience in such situations. The effect is due to decreased blood flow, but not because of an inability of the heart to raise blood to that level, but because of increased vascular resistance. This is a subtle but important difference.