I've been lifting weights a few months now, and my veins seem to stick out more than they used to. I don't think my body mass or body fat has changed much... it just seems like my body, especially arms, are veinier than they used to be. Is this actually a thing?
This is a bit simplistic, but when you lifts weights your muscles get flooded with plasma. This increases the tension within the muscle itself and this tension pushes the veins closer to the surface.
The old explanation was that it was due to an increase in blood pressure, but this has been debunked since pressure actually decreases when we exercise, due to vasodilation among other factors.
BP may spike when performing a lift, but it quickly settles back down -- the veins bulging sticks around long after.
As far as actual improvements in vascularity, like capillary density....that's a good question. You'll often find answers going both ways to this question. But the best research I've seen that clarifies this states that in the weight lifting condition capillarization may occur, but proportionally less than hypertrophy. So the number of capillaries may increase, but the overall capillary density may decrease because muscle growth outpaces it.
Hope this helps
The most probable explanation is a reduction in bodyfat %.
Even if your whole-body bodyfat % has not gone down, if you have added muscle to your arms, the same amount of subcutaneous fat (and skin, especially if you've gained muscle quickly and recently) will be spread over a larger surface area.