Does the weight of the shoe affect how far you jump?

For the same leg strength / jumping technique, weight affects how far one can jump.

Acceleration = Force / Mass

With more mass, you cannot accelerate yourself as much when you jump with the same force. Imagine trying to jump with a small backpack full of sand strapped to your back. Your strength hasn't changed. That is, the amount of force you can deliver hasn't changed, but your mass has. You can't jump as high.