Visible veins after lifting are a natural biological reaction to exercise.
It's reasonable to presume that an increase in blood flow when exercising would make your veins expand and be more visible under your skin. However, it's not increased blood pressure in your veins that makes them rise to the surface of the skin.
When lifting weights, veins bulge to the surface of the skin because of increased plasma causing the muscle mass below to swell and harden.
Set the Stage for Bulging Veins
When you place stress on your muscles by weightlifting, they naturally respond to the strong stimulus. For the first 10 seconds or so, the muscles break down phosphocreatine that releases the quick energy needed to meet the demand. As you continue working out, your muscles turn to breaking down stored glucose. Initially, your body can do this without the need for extra oxygen, but after a few minutes, your muscles cry out for more oxygen to break down glucose into ATP (adenosine triphosphate) to power the demand of lifting the weight.
Your breathing comes faster and harder; your heart pumps faster, delivering more oxygen-rich plasma and blood to the muscles. The increased load causes your arterial blood pressure to rise, pressing the blood into arterioles and then into capillaries as oxygen-rich blood and plasma make their way to the site of exertion. As plasma floods into your muscles, it causes swelling of the tissue as it makes ATP to provide energy. Veins push to the surface of the engorged muscles, making them appear larger.
Bust the Myth
Carbon dioxide and other byproducts of the ATP-making process re-enter the bloodstream, getting carted away by veins. As your blood returns to your lungs and heart, the pressure of the blood is far less than that of the arteries - just a few mmHg in the veins as blood returns to the heart compared to as much as 345/245 mmHg arterial pressure during squatting while lifting weights. The relatively low pressure in the veins isn't enough to make them pop out.
Those Sweet, Stand-Out Veins
For several hours after working out, the plasma-engorged muscle pushes your veins to the surface, making them more prominent. The lower the amount of body fat you have between the muscle and the skin, the more noticeable the veins appear. Arms and hands will appear especially vein-y after an upper body workout. After a lower-body workout, you're most likely to notice bulging veins in your feet or over the ankle bones.
Those with unusually low body fat will notice bulging veins even when they haven't worked out. Toned muscle plus low body fat causes the veins to be more noticeable even when you're at rest. Your genetics also play a role in how vein-y you appear.
Consider Your Health
Bulging veins can occasionally be a sign of health issues, though. Varicose veins and hemorrhoids are two examples of bulging veins that indicate a deeper health issue. Excess stress can also swell veins as the stress hormone cortisol causes increased sodium levels and water retention. Because weightlifting causes a significant increase in arterial blood pressure, don't lift if you have uncontrolled high blood pressure.