How much should the average 14 year old 5'2 female weigh?

About 102 lbs. The weight at same percentile for height for an 14-y-o girl would be around 102 lbs.
Average =100lb. The regular range would be about 100 lb using cdc growth charts. You can download a growth chart and keep track of height & weight on your own. See ww.Cdc.Gov/growthcharts.