Pigs DO come in all shapes and sizes, and as such, 1200g for one pig maybe ok, 1200g for another pig may be far too much.
I had 2 litter mates, Big Dave is 1400g, and is a good healthy weight. Boxy was 750g and also a good healthy weight. If Boxy was 1400g, he'd be horrifically obese.
Guinea pigs, like any other animal, can become overweight. Plump/chubby/whatever may be cute, but is it healthy? I don't think it is! My Jeff has been on a diet (restricted pellets and carefully chosen veg!) as he was too fat in my eyes.
Overweight animals (be it an elephant or a mouse) find it harder to cope with an anesethetic, and an overweight animal can be more likely to need one!
The fat that you see is subcutaneous fat, fat that is stored under the skin. The dangerous fat is the one you can't see - visceral fat is laid down around the organs and it's that that causes problems, particularly for the heart and liver.
Personally, I think guinea pigs can be too fat, and I have strived to (try!) and make sure that mine aren't!