The quads are some of the strongest muscles in the body. They carry your weight all day, so you may not see results from squatting body weight on both legs.
You could try pistol squats. They're hard as hell, because you're squatting your body weight with one leg, but if you can do them, you're pretty hardcore.
Otherwise, I recommend you pick-up a weight set. You can do squats with dumbbells, but you won't get past parallel since you're arms are hanging down, unless you can get them up on your shoulders, but you probably still won't have as much weight as you could with a barbell resting on your back.
Here's an elaboration on what I said before: performing the concentric on an ATG squat is almost entirely glute activation up to the parallel, after that it's largely quad. If you want to work your posterior chain, you want to do deadlifts. Romainian deadlifts and straight leg deadlifts are very good in this area.
One of the regulars on MH said he did lose has ass for a while as he lost the body fat, but it came back solid as he kept doing them and muscle grew.