I think smiling at people should be encouraged. Not a great way to meet people though since people aren't just going to talk to you as you walk by because you're smiling. Though, if someone is hesitant about talking to you, smiling will definitely negate that feeling.
It may be a bit surprising for a second, but then it's a sign of friendship and invitation to communicate. I was sitting in class when a girl sat not far from me. I looked at her a minute later, and saw her looking at me with an added smile in one second. It made me feel happy that someone is welcoming me. The next class, she sat next to me, we started talking, and became friends. Smiling is a great way to invite someone to be friends with you.
It's not weird at all, at least not to me. I believe it's only polite to do so ! The only times I do not smile to people who look at me is when they're glaring at me or if I really don't like them. Even then, I might juts smile harder at them to laugh at their hate :P
I don't think it's the best way to actually meet new people though. You could always go talk to someone random from one of your courses and start having small talk everyday.
Otherwise, I suggest signing into an activity you like, and try to get to know people in here :)
Smile! I think it would be weird to make eye contact with someone in passing and not smile. I don't know if it will actually help you make friends, but smiling makes you seem more friendly and approachable, and that could definitely help.