Are heavy weights necessary for muscle growth

If I do (pushups, dips, squats and lunges) for example, will I gain muslce?  I want to get stronger, but I'd also like to develop a bit more muscle.  Thanks 

 What is required is progressive overload of your muscles - lifting more than 70% of your 1RM max to be exact, adjusted upwards as you get stronger.

 If you can't do more than 20 pushups it's still strength training for you; and if you can do more you can put your feet up on a chair and see how many you can do that way.

 If you can do 20 lunges in a row (per foot) - move to doing step-ups ore one-legged squats.

 Pleny of ways to provide increased resistance without external weights, they're just more convenient. And if you do need external resistance, anything heavy will do - backpacks with books, shopping bags with soda bottles, small children --- anything that's light enough to move and heavy enough that it gives you a training effect.

I've heard a lot of arguments that using one's own body weight is the best resistance, especially if you're starting out.  But as melkor said, if it's not hard, it won't be doing much.

Also keep in mind that building muscle and building strength are two different things, you can gain strength through exercise, but you need a calorie surplus to gain muscle mass (size AND strength).