I'd say between 9 and a half and 10 stone, something like that? And that's not average weight, by the way, that's 'normal, healthy weight'. Girls that age and height can be anything from 8 stone to 12 and still be average.
Build and fitness will also make a difference, though in men more than in women.
This is because extra muscle weighs more -- and it's much denser than fat. A woman friend of mine is a good amateur triathlete. She is superbly fit and has an excellent figure, but she weighs perhaps a stone more than you might expect for her height.
I do try to claim that my own extra avoirdupois is all muscle, but no-one else seems to listen...
The main thing is not to get too hung up on weight itself. Plenty of attractive and happy people are far above or below their "ideal" weight. Concentrate on keeping reasonably fit and being happy.