This is a really cool idea and you did a good job implementing it. I had a lot of fun playing!
On level 2, my browser crashed. It looks like something in your code is probably causing a memory leak, the framerate steadily dropped until it froze then crashed. ( for example, maybe something is creating objects over and over, etc. )
Overall a really fun and expandable idea. Being able to grab a platform and take it with me was fun.