Don't be silly, there's something wrong with everyone. There is no such thing as "normal people", everybody's screwed up in some way and that's perfectly fine.
That said, if the only thing that makes you think she's a "weirdo" is that she's interested in you, it sounds like you're just making excuses for yourself to not step outside of your comfort zone and give it a shot.
THIS ^^ Exactly that.
For further elaboration:
I haven't had a girlfriend in almost 9 years, and even back then it was less than a month and we only kissed twice. Had no other relationships before or since and I doubt there was any point where she was committed to that relationship anyway so I'm sure that barely counted as is.
a relationship is a relationship. Whether it be a few weeks or a few months or a few years. I've never had a relationship with a guy last over 3 months and be healthy. I had one "relationship" (and it's in quotes because it was basically him using me to cheat on another girl, to emotionally manipulate and abuse, to verbally abuse, and to basically make me feel absolutely worthless and dependent on him and that lasted almost 5 years and it was technically a off and on we're dating/we're not dating thing) last longer but that was abusive and unhealthy as shit. I had 2 relationships that were healthy. One lasted a bit over a month. Why'd we break up? Simple. His mom was going crazy(bipolar and depression. always a great combo), my family was being their usual insane selves and 10x more demanding, and the place we both worked was going crazy with schedules due to holidays coming in(we dated all through october and slightly into november)and we honestly didn't have the time nor the energy to put into a relationship. He and I are still best friends and talk/play video games fairly regularly. The other healthy one I had was the 3 month and we broke up because he wasn't sure he could respect my wishes for staying a virgin past 3 months given his history and didn't want to try and force me into a situation I wouldn't want to be in. Also there was the whole "I don't want to get married/have kids ever" conversation and he wanted to get married right out of high school and have kids. We're still good friends and he got his wish. I couldn't be happier for him. Point is, just because someone isn't committed to the relationship doesn't invalidate it as a relationship.
I've had interest in a few girls since then but none of them shared the same feeling. But oh well, no big deal. Not like it really mattered much to me anyway, too busy to keep a steady consistent relationship anyway.
It kind of seems like it matters a little to you since you mention it.
But then the other day a girl suddenly showed a little interest in me. Now I'm sure it wasn't anything serious but it took me a bit off guard and it made me realize that I can't imagine myself being interested in this girl anyway, she's most likely a weirdo.
Point me to someone in this world that isn't a weirdo. Everyone is to someone else or some extent. Some people hide it better than others. Was she weird just because she showed interest in you? no. She was weird because you perceived her that way. To be honest, I don't believe there is anything that can be universally considered normal as far as humans go.
Could you not imagine yourself being interested because you perceived her as weird? Or because she actually showed interest? And what kind of interest did she show?
Because honestly. I'm sure I'm just not an attractive guy, experience has shown that girls don't care about me. So at this point I think if there was a girl who showed interested, I'd feel there's something wrong with her more than me.
Most people believe they are not attractive. Hell, I have this argument weekly with one of my guy friends. He believes he is unattractive(yet he fails to recall unless convenient for him of course, how many times I've flat out told him how attractive I find him and other girls have found him)and we argue that back and forth and I believe I'm unattractive and he tells me I am but refuses to tell me how I am. Of course then there is also our other weekly argument of who looks better topless me vs. him. I, naturally, find him more attractive topless than myself but he just doesn't understand my love of men with chest hair and stubble on their faces and who are adorable gingers and who are my best friends and enjoy scaring the shit out of people and who team up well with me to scare the shit out of people.....umm yeah back on topic. It's not exclusive to men or women to find themselves unattractive. It's a society wise problem. If you feel there is something wrong with a girl just for showing interest in you, that's more a problem with you. And it's more rooted in your own self esteem. Would you feel a girl was weird because she showed an interest in talking to you because she found you particularly interesting? And seriously, don't you think girls have it bad enough society wise that we also have to worry about being "weird" according to someone we may/may not be attracted to/interested in? There are many levels to being attractive. It's not all just physical. Really. I'm more attracted to people based off their intellect and their ability to make me laugh and feel comfortable.which is why i have a huge thing for my best male friend Physical appearance comes down near last on my long list of things for me to find someone attractive. And as I am attracted to humans in general and have a different view of physical attractiveness than most of society......I've dated some people that others upon seeing them have gone "what the hell would you date someone that ugly for" and vice versa, I've dated people that go "there's no way you could have dated someone that attractive". Believe me when I say, some of us truly don't care about your physical appearance as long as you have good hygiene.
Just because some girls didn't like you doesn't mean all girls, as a collective, won't. Maybe she just likes different things? Why is this a problem? And just writing her off as 'weird' for wanting to get to know you seems like there's something wrong with your self-confidence (not you per se). Give her a chance before moving on, you might even have some fun.