I myself am a big fan of this feature, which, to my regret, is not very common among men. I read that veins become pronounced as a result of a set of muscle mass, by men whose weight was below average (more often ectomorphic physique). And yet such veins are found in men of different types, which indicates the fallacy of this assumption. It seems to me that sympathy arises from associations. Most women are impressed by men of a large physique, that is, the larger the organs of a man, including his blood vessels, capillaries, etc., the larger he is, and therefore stronger, therefore more dominant, and therefore more attractive.
The love of veins can be associated with the popularity of Tumblr and the aesthetics popular on this resource (sorry for the tautology): blood, cigarettes, knocked knuckles, cuts, bruises, translucent skin, and so on.
Also on the Internet among teenagers a popular topic is the so-called. selfharma - inflicting pain on oneself to calm down and release inner tension (the topic of selfharma is huge, I covered the part related to my answer). The most common option is to cut your veins, and contemplating beautiful wrists with transparent veins also has a certain effect on them.
Quite a strange phenomenon, but I can assume that in the veins of girls they see some kind of brutality, strength (along with pumped up arms; no, well, really, I have never seen pronounced veins in overweight men). Well, plus the fashion, which very quickly inspired the girls that the veins of the guys are incredibly cool, this makes his masculinity stand out (well, if it cannot manifest itself in anything else). I cannot find any other logical explanation.