"My ride is a 2004 Giant OCR2 and I do nearly all of my recreational riding in East TN. This area has a lot of hills (I moved from FL about 4 years ago and I still haven't gotten used to them). Anyway, my bike is a triple, but I'm wondering what makes the biggest difference when you're riding in an area with lots of hills. Some guys in this area say that you can't tell the difference between a double with a light frame and a triple with a heavier frame. True? Is there a road bike that is manufactured specifically for hill climbing?"
What makes the biggest difference:
Being in shape. A couple of pounds on the bike is nothing compared to the tens of pounds off of you, and a doubling or tripling of the available power.
Gearing will get you in the cadence where you are efficient and make power, and out of the range where low cadence will injure you. Gear for 90 rpm or above on the steepest grade you will encounter. If you don't use it, good, you had a spare gear.
I recommend a triple, especially for your age group. Gear it the way you need it now, and change it if you need to later. I always gear so I have the ends of the range I need, and the most gears possible in between.
When you have thin skin and strings/cords/cables for muscles, and you can see your hip bones / ribs / collarbones, you are getting in shape. Heart rate in the middle forties or lower?
Had one of those treadmill stress tests down at the cardiologist's?
Quickie back-of-the-envelope calculations suggest that to be in shape at 225 lbs, you'd have to be about 6'8".