I don't see why people think that weights are used for increasing strength, they increase speed.
I have used weighted training clothes and belts like Lee has and the main focus to using that is to increase speed, and in some instances, jumping if they're warn on the bottom portion of the bottom. However, the added bonus to wearing those is an increase in strength, but no by much. The only way you'd see a large increase in your strength (kicking or punching) is if you continuously increased the amount of weight that you're wearing. Even then though, there is a maximum limit to how much you can wear that your bodies muscles and bones don't suffer too much problems in the future.
Now, the only reason that the increase in strength is probably seen so much in Lee is that the amount of weights that he is using in the Naruto Universe is unreal. As we saw in Part I he had weights that practically destroyed the floor below him when they dropped, but that's pretty difficult to achieve in real life. So technically, Lee's strength while wearing those increase enormously because he was able to put over 500+ pounds on him.
Real Life = Increase in Speed
Naruto Life = Increase in Strength
We'd literally have to put as much weight as Lee did to increase our kicks as much as we would when we'd do squats.