Average weight...?

The thing you must look at your age and your bone size. If you can wrap your middle finger and thumb around your wrist with them just touching, you're average. If your fingers overlap, you're small-boned. If they can't meet, then you're big-boned.

Judging from all that, you look at the BMI (Body Mass Index).
You look at your weight with your age and bone size and it gives you a number.
* Underweight = Less than 18.5
* Normal weight = 18.5-24.9
* Overweight = 25-29.9
* Obesity = BMI of 30 or greater

So a BMI of 21 would be smack in the middle of normal weight, so 115 lbs (given that you also have normal bone size.)

Here is the chart:
http://www.nhlbi.nih.gov/guidelines/obesity/bmi_tbl.htm

If you just want to know the average weight, here's another chart:http://www.halls.md/chart/height-weight.htm

Keep in mind weight is a tricky thing. How much muscle do you have? Muscle weighs more than fat, so it's hard to just look at an average and say that's what you should be. You should just look at what weight you'd be the healthiest.