Had a Cat 1C on the Millennium in February. As you go down on the aft balconies, they get bigger, so I'd suggest a 1C, the balcony was 241 sq ft I believe. The rooms was a great size, not as big as a Cat 3, but plenty of room!
We had cab 9201 (1A) on the Infinity. The cabin was a nice size, but the balcony was the selling point. Really big. We were offered an upgrade to a suite and when we checked the balcony with the suite we happily went back to 9201. We checked out the Cat 3 next to us and the room was bigger and had more goodies (2 TV's, vcr etc). We were able to get a Cat 3 for next April on the Summit. Our agent couldn't believe how fast they were selling out! If we couldn't have gotten the Cat 3 we would have happily taken a 1A or 1B off the aft. I can't believe Celebrity didn't make all the aft cabins suites. But I'm not complaining, the price is reasonable.
The corner Cat 3 balcony is 241 sq ft -- the aft 1's must be about 100 sq ft.with the 1C's being smaller than the 1B's and 1 A's. The aft 1's are a real bargain, I think -- nice sized balcony. Just not quite 241 sq ft THAT nice, .
For a great picutre of the Aft cat 3 cabins, check out the post "Photos of the May 1 Infinity cruise" posted by "jeff". I had the thrill of hosting this group on my BIG balcony! We were in cabin 9197 which was a corner cat 3.
The aft-facing rooms that are not Cat 3 have slightly smaller balconies than the 3's, but not much smaller. They're still huge, and as has been said, the real selling point for the aft. The point about Cat 3 rooms vs. aft 1 & 2 is that the 3's are obviously intended for families with one or two kids, or perhaps young adults with their parents, etc. It isn't just that they're bigger, they're configured for more sleeping area. Naturally, to obtain this, there are some design compromises, but for a ship they're minimal. I think that sometimes it's important to think about what you're trying to accomplish by booking a particular room, and not just square feet. Cat 3's are great for three or four people. Booking one for two people would really have no great advantage over an aft 1 or 2, except that you'd have to walk farther to get to the balcony.