How to stop weird labmate from staring at me doing experiments without damaging work relationship (too much)?
It's more of a comment, but I just want to voice that in my teaching career, I did encounter a couple people with these traits and they do have what we called Autism spectrum disorder (ASD). I am not diagnosing OP's colleague, but I'd like to suggest this possibility, and we should be mindful that it may not be fair to assume the person of question can fully function socially.

After talking to faculty and doing some homework searching for resources, what I found useful was i) talk to the person privately about your expectation, and ii) be direct, don't use social hints. In many ways it's not that different from what other users suggested you to do, but I'd just like to add another point that sometimes some people can appear to be rude because they don't know it's rude, not because they are rude.