How to deal with a leech student?
Your time is yours to control. If someone just wants to meet to learn about your field, it's polite etiquette to give them a brief meeting and let them learn... it is a learning environment, after all. It sounds like your situation has progressed well beyond that. I would simply tell the student that due to your own time constraints you cannot continue meeting with him. Consider redirecting him to the department chair/administrators, where he can ask about the process for joining a lab.

For what it's worth, if it's really beyond academic interest and he's just a stalker, that changes things a bit. Definitely work with whatever resources  your university makes available to figure out how to deal with a stalker.