Which blood vessel type has walls only one cell thick?

Capillaries are the smallest vessels, so narrow that red blood cells often pass through in single file, and their walls are a single layer of flat cells. That is not a weakness but the entire point, because everything the circulatory system exists to deliver has to cross the vessel wall somewhere, and it happens here. Oxygen and nutrients diffuse out into tissue while carbon dioxide and waste diffuse in, driven simply by differences in concentration over a very short distance. Arteries and veins are just plumbing by comparison. Capillaries are also extraordinarily numerous, forming dense beds so that almost no living cell sits far from one, and their combined cross-sectional area is so large that blood slows right down as it passes through, giving time for exchange. Rings of muscle at the entrances to capillary beds open and close them, which is how the body redirects blood to working muscle or to the skin to shed heat.

The lungs carry the densest capillary network in the body, wrapping the air sacs where gas exchange happens.