consider their functional differences why do you think the walls of arteries are proportionately thicker than those of the corresponding veins

The veins and arteries encounter differences in the pressure of the blood flow. As a consequence, these differences are seen in the composition of the vessels. The arteries encounter with a pressure wave as blood gets pumped from the heart. This can be experienced as a pulse. Due to this pressure, the arteries' walls are much thicker in comparison to those of the corresponding veins.

Thus, arteries appear to exhibit more uniform shape, they seem to be more circular in shape in comparison to veins. Veins do not encounter with the pressure waves like the arteries do. Thus, they do not require to be structurally strong. The vessels' walls of veins are thinner in comparison to arteries and do not exhibit much tunica media.