Sensory Integration theory supports what you guys are talking about - how movement actually SUPPORTS learning. Jean Ayres' theory states that sensorimotor development is critical in the development of higher level cortical processing. That's why little kids need to move! And the use of the weighted blankets or lapbuddies isn't to "weigh them down" - it's to increase proprioceptive input, which is a calming/organizing sensory input (the sense of our own body, perceived through sensory receptors in our joints, muscles and bones). The same is true for using a large ball as a seat (or other types of alternative seating/positioning). It taps into our sensorimotor processing with both the proprioceptive and vestibular systems.
What you know to be true intuitively is actually well rooted in neurological theory - that most pediatricians and educators don't even know about! A good parent/teacher resource is the book SI and The Child, by A. Jean Ayres, PhD. She is the OT who developed the theory and practice of Sensory Integration.
(just a little fyi, with my OT hat on!)
