This is my brief opinion about bigger arms:
IMO the arms will grow in direct proportion to overall body mass/body weight increase within an appropriate diet and weight training routine (I am speaking in terms of a healthy and normal human being).
Do not think for a fraction of second, that if you do direct arm work, and neglect the other major muscles of the body and NOT putting on "appropriate weight" will build massive arms, because it will not.
They will grow to a certain extent (especially strength and growth when one first starts out), but not near the extent if one were to put on some body weight and train: the legs, the back, and other major muscles of the upper body.
What does you entire routine look like? Diet?
Chillen