Why do different blood vessels have different lumen sizes (relative to their overall size)?

Lumen sizes in blood vessels differ due to the differing functions of the vessels themselves.

Arteries have to carry oxygenated blood away from the heart to the tissues at high pressure. Small lumen (relative to the large, muscular vessel) ensure this pressure is maintained as the blood is transported around the body.

Veins carry unoxygenated blood towards the heart, away from tissues at low pressure so the lumen is large. Blood moves more slower and often against gravity so valves and a larger lumen ensure it is still transported efficiently.

Capillaries have the smallest lumen but relative to their size the lumen is quite large. This is because capillaries are where exchange of oxygen, nutrients and waste products occur between blood and tissues so they have evolved to have the greatest surface area to volume ratio to increase efficiency of the exchange. This involves there being many many capillaries which are very small with walls only 1 cell thick.