I've got a theory about why it works. Basically you're tiring out parts of your brain when you exercise and activating others. Somehow that regulates the neurotransmitters at the heart of add for a while. If I only lightly exercise, I don't get the same effects. The workout has to be strenuous and I need to feel like I worked both body and mind (finishing that last rep under heavy load takes willpower and concentration).

I bet that HIIT could be as effective as weights for me because the curative part seems to come from exhaustion and exercise of will.

Meditation may or may not be as mentally strenuous, I am not really familiar with it.