I don't think there's any way to predict your bodyfat at a given weight. It really depends on how you work out and eat.
When I hit my initial goal weight of 135, (I'm 5'3" also) I had been doing cardio 5 times a week and circuit weight training 3-4 times a week. I wasn't lifting light, but I was doing a fast paced full body workout at home, each time. Excellent for burning calories, poor for building muscle. At 135, I was dismayed at how squishy my body looked. I don't know what my body fat % was at that time...best guess is around 28%. I started doing the Body for Life program and after a month decided to join a gym. After a month, my weight was still 135, and my body fat was measured at 27%. I already looked a bit different. After the first 12 weeks of Body for Life my body fat was measured at 22% and I still weighed 135. I was a size smaller. Three years later, my weight is now 122-124 and I range between 16.5-18% body fat. I lift HEAVY five days a week, a different body part each day.
My measurements are based on a 9 point caliper test, not a scale. I think the scale measures slightly higher the older you are.
You had two categories in your post: fat skinny or lean skinny. I would rather see women aim for a third altogether: lean and muscular! Lean skinny is bony, hard to maintain, not all that attractive, and puts you at risk for a lot of long term health problems. Muscle protects against alot of those problems. Don't worry about a few extra pounds of they are muscle! I'm sure If I stopped lifting or cut way back, I could drop five pounds easily, but who would help wrestle the couch out of the basement? I'd have to say "yes" when those obviously weaker 16 year olds at the grocery store ask if I'd like help taking the bags to my car

I don't want to be one of the frail, bent old dears in a nursing home in twenty-five years!
Mel