What is appropriate weight for a 14 going on 15 teenage girl?

Depends. That totally depends on puberty status and height as well as height potential and activity level. Every girl is completely different and there really is no standard weight gain or weight goal. Talk with your doc and ask to see your growth chart. What is most important is using that chart to compare your rate of weight gain over years. See if you are gaining steady, or too fast or too slow.
Average Weight. 5' girls ideally weigh 100# and for every inch increase add 5#, so a 5'2" will weigh 110# as long as you are healthy be happy.