Each person is unique and responds differently but generally for each 10-15 pound gain in muscular bodyweight you should add about one inch to your upper arms and close to one half inch to your forearms. (Note: I stress muscular bodyweight -- adding 10 pounds of fat is useless and as mentioned earlier, will just hide your muscularity and make your arms look smaller and less impressive).
If you are genetically predisposed of big arms or of superior genetics you may gain even more, but if you have poor genetics your gains may be somewhat less. Usually one inch per 10-15 pound gain holds true in most cases.
No matter how good your genetics are it takes time to build such size. You may gain 20-30 pounds in your first year of training and then 7-10 pounds your next 3-4 years, and then it may be difficult to add even 5 pounds of muscle a year, so to add 4-5 inches will take years.
If you currently have a 14 or 15 inch arm and weigh 160 pounds don't expect to build your arms up to 18 inches some day and still weigh 160 pounds. It's a physical impossibility.
Face it, every "big arm" champ from Park, Pearl, Draper, Scott, Sergio, Arnold, Beckles, etc., are huge people and all weigh over 200 pounds in top shape.
Don't believe that garbage about Mohamed Makkawy, Franco Columbu and Danny Padilla only weighing 170 pounds or so and having 20" arms. It just ain't so. Most arm measurements are grossly exaggerated.
At last year's Olympia in Munich, Germany, Makkawy's arms were 17.75" but because of his shortness and incredible cuts and symmetry most people would swear his arms were at least 20 inches. Likewise for Danny Padilla. Several years ago Arthur Jones measured Franco Columbu's arms and they measured 16.75 inches cold. These are true measurements. A real 18" arm is huge.
Remember too that those guys are the elite of the sport; the guys with the best genes. If they can only manage 17 to 17.75 inches [with assistance] should you expect more? Hardly!
Very, very few guys can build up to a muscular 200 pounds and build a 17 or 18 inch arm let alone build up to a muscular 220 or 230 and have 20 or 21 inch arms. It's rare, believe me.
Even Arnold has his limits. Once he went over 235-240 pounds he started smoothing out and looking fat. Likewise you may find your structure only allows you to weigh 190-200 pounds and anything over that and you lose your shape and cuts and look fat and if you have a small frame even 170-180 may be too much for you, so you'll have to be content with a smaller arm.
But even as 16.5 or 17 inch arm that is well shaped and symmetrical with cuts and separation is far more impressive than a 29 incher of shapeless, smooth bulk. As they say, you can't flex fat.
I'm not saying not to try and build you arms as large as possible. What I'm trying to tell you is that size is only one quality of good arms and if genetics won't allow you to build big arms, then build the best arms you can by concentrating on the other essential characteristics-- like shape, balance, separation and cuts -- and your arms will still be very impressive.