For reference, this is what my arms looked like when I was in my best shape (at 150lbs in 2009). I did a serious arms weights workout, at the time, which is how they got that way. Even though I did bicep curls with a 40lb. barbell, they didn't get any bigger.
This is what my arms look like, now, at 167.5lbs, and just getting back into working out:
I hope to get back to my previous arms, and am doing weight training to get there. Good luck!