Body weight squats will increase your leg strengths initially. If you don't run or play sports that require running, you should experience some strength in your legs (quads, glutes, and calves). However, if you do perform these sports, you won't really experience an extra benefit to body weight squats.
Frankly, body weight squats is more of a cardio exercise than a strength exercise. It'll build endurance and agility in your legs, which will allow you to perform better in sports. But it won't make your legs bigger.
Based on the information retrieved from the comments, it seems that you have access to equipment; the problem is that you can't perform activities that involve putting heavy weights on your shoulders.
As a result, I wouldn't really advocate barbell back squats for large weights (because of the potential injury if your shoulders fail).
Goblet squats is a good idea. You can increase the weight, which will help your legs.
Dumb bell squats
is another great idea.
Caveat though: your grip strength partly determines how much you'll be able to go.
This form of dumb bell squat is also great (depending on your shoulder strength though).
Leg Presses: You cannot go wrong with leg presses.
That can build some serious strength and muscles on your legs. No shoulder required :).
You can also perform many calf exercises, leg extensions, and other machine-based exercises.
There are more exercises that you can perform....but you get the picture :).
You are not limited to only body weight squats. :)