The current setup does something quite similar: It uses a tensioner to pull all three sheets (kinda like what the weight would be doing in your scenario). Unfortunately, using gravity is not an option due to the machine's stupid layout. So... instead of letting gravity do the work of aligning it, I have to find a way of manually lining everything up... Ugh, I really hate this machine.
Out of curiosity, can you/anyone recommend a good analog LDR with good resolution in a small package? I'm along the lines of using a cheapo laser, pass it through a filter, pass that through a pinhole (to decrease the size of the dot and increase accuracy), and have the LDR detect the tiny remaining LED dot. Am I on the right track here?