Only you can decide what a "reasonable size" is and if you're happy with that and your actions will be based on this.

That said, it is very hard to only build up your arms ... not to say it's impossible. I believe you should focus on building up your entire body as a unit. Strong arms mean nothing without strong legs to push against and tight core to transfer all the force. Become big and strong requires LOTS of eating and lifting heavy with compound movements.

IW