Why do some white people stare at me and my white girlfriend?

I believe that there is not just one answer to your question, but rather several answers, as there are several people who have "reacted" in different ways to you and your girlfriend. I think you are too young to have seen the movie, "Guess Who's Coming to Dinner?" with Sydney Poitier. He payed in some very powerful movies. Google him and watch his movies, and learn from his Life (Google or Wiki). The couple who giggled might have thought you two looked cute together. Don't always assume the negative. Your girlfriend looks like she would attract anyone's attention just because of her good looks. Perhaps she is aware of this, and enjoys the notoriety or the attention. Those older people at the gym are mostly jealous. Some people would be prejudiced because in this world there are people who are jealous for one reason or another, So basically, some people stare because they are prejudiced, some because you two look cute together, your girlfriend attracts attention because she is cute and pretty, and most people are just jealous of you. There is a phrase that was going around when I was younger and it has nothing to do with skin color, but is apropo to your situation. You need to develop some "tough skin".as it sounds like you have "thin skin." Life will be hard enough by itself, so make up your mind to live your Life with a sense of wonder and joy in your heart, and let the obnoxious people drop by the wayside. Good luck to you.