What can visible veins all over my body mean?

Usually normal: Prominent veins are often normal.They are more visible in thin or fair skinned people. To be safe, especially if you have other medical problems or symptoms see a doctor.

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.