Is it weird to eat at a restaurant alone?

No. I eat alone in a restaurant quite often. In fact, I just did so yesterday around 5pm. And I don't care if people think that's odd.

I've seen people do it and never questioned why. Sometimes people just want a quiet meal in public to themselves.

Exactly who is going to give you strange looks? I traveled for my job and spent many nights out each year, so I would always have dinner and sometimes lunch alone - it's actually very relaxing.

Depending on the type of restaurant but most restaurants usually have bar areas and I'll go sit at the bar. I've had no problem doing that and always get great service from the bartender.

No. People have all sorts of reasons to eat alone.

I go eat alone at a restaurant every single day of my life.

No, it is not. I do it from time to time ( e.g. when I have lunch time at work) and it is perfectly normal.

No, not weird at all. Lots of people eat at restaurants alone. In fact, in cities around the world, it's common for single people to have different "haunts" where they like to go and eat and/or have a drink of some kind while doing something like cruise the internet, or look over e-mails, etc. Usually it's more common for them to go to more casual places like diners and cafe's, but they'll make use of fancy sit-down restaurants too, if they feel like it and can afford it. In that situation, it's not unusual for the single person to make friends with the people working at the restaurant if they're a regular; particularly if it's a family-owned restaurant.