Background/Qualification: I'm 5ft 5in, 25 years old and I have a 3 plate, 3 rep squat maximum (3 reps @ 140kg/315lb) at 75kg bodyweight. My thighs/quads are BIG, if i'm standing straight with my legs together then my quads are wider overall than both my waist and hips. I don't know anyone my age and height with legs comparable to mine (who isn't obese/powerlifter), i'm hovering at around 17-20% bf (estimated).
If you want big thighs then you need to eat big and squat big. I can guarantee you aren't eating enough.
Provided you are starting lean (<20%bf) and have the ability to eat around 3000 calories a day and workout for a hour and a half 3 times a week then you are all set:
To improve your muscle size, you need a equivalent to a barbell program. Grab a piece of scaffold and tie on some water jugs or grab a heavy object and do front squats. The key is that you need something you can add a small amount of weight to every time you work out:
"Correctly designed barbell training programs take advantage of the
fact that barbells can be incrementally loaded and gradually made
heavier, thus forcing the body to gradually become stronger at a rate
that can be supported by each individual. If you only use your own
bodyweight for the resistance, it severely limits your ability to
tailor the resistance to meet your current level of adaptation, and to
gradually increase that adaptation so as to improve your strength in a
predictable, directable way". Mark Rippetoe
Bodyweight and barbell programs will both make you strong, there are many stories of people who don't weight train and end up lifting very large amounts their first time out, due to body weight skills. Here is a video of Ross Enamait deadlifting 495lbs (at 170lb body weight) with no deadlift skills and a primarily bodyweight-only training routine.
But to get BIG you need a barbell (or equivalent) and a big diet, this is why bodybuilders do mostly barbell work and not mostly bodyweight work. Take supplements (creatine/protein) if you need it but you should be tracking your diet and understand you macronutrient breakdown to see if you do.