During pregnancy, especially early pregnancy, your breasts may become veiny. A more accurate description might be that the veins already in your breasts merely become more visible.This is because your blood volume increases 20 to 40 percent during pregnancy. Your veins are transporting blood, nutrients, and oxygen to your developing fetus. The increased blood volume makes the veins more visible under the skin. This typically lessens after you give birth, but it can persist afterward, especially if you breastfeed.