I'm 18 and have been overweight since I was around 8 years old. Before that, though, I had a very petite frame. My question is, once I lose the weight, will I still have a small frame or will I never be able to be petite again?

you will most likely have saggy skin you may still have the small figure but with large masses of skin

It's hard to say.. You're body at 8 years old will be nothing like your body at 18 tnow that you've matured... Take a look at your family/parents/aunts to get a gauge on how you may be built...
Regardless, you will feel amazing in a leaner / healthier body! Keep up the good work!!!

Your body will be totally different now to what it was when you were a child. However go for it and lose weight you will feel on top of the world.