From an anatomical perspective, veins do nothing for erection, stiffness, or size. Veins by definition carry blood to the heart. Thus, speaking very generally, they would be responsible for deflating an erection. In general, veins tend to run near the surface and arteries near the core of whatever appendage you may discuss. In essence, visible veins are simply eye candy for those who appreciate them. Stiffness and length/width are really a function of genetics, not only in just sheer size but also in function relating to nitric oxide regulation for generating erections.