Females are in general much smaller than males, for example I was at the humane society here today and they had five rats. Three hairless males (3m) and two females (American Blue berk and Mink berk, 1y). The males were bigger than the females.
And if you try and take into account dwarf rats... :lol:
I'd say that around a year they're adult, but I know some rats put on more weight when they're older as a 'cushion' against age, etc.
It also depends on the rat. Our first girl was a slow grower and didn't reach her full size until about a year old. Our second girl was as big as our first girl when she was 3 months old! We thought she was going to be enormous, but she seemed to stop growing after that. She is just slightly bigger than our first girl, now (at 8 months old).