I have "abnormally" large veins. Occasionally, my veins bulge. Is there any medical reason to explain my increased vein size?

Probably normal. Veins can enlarge and shrink for many reasons most commonly levels of hydration, genetics, aging, sun exposure, temperature changes and even skin color being more prominent in fair skinned people. Most commonly what you are experiencing is a normal variation but you probably should see a vein specialist for a full venous evaluation so that they could examine you and answer all of your questions.