I have this same logic as well. One time in my art class I was talking to the girl who sat next to me and we had a whole conversation on being normal.
All I say, is that normal is what is typically accepted and typical for that period of time. Weird is what is out of the ordinary, or not normal, for that time. So basically, being normal depends on what people believe in.
This can change though, because thoughts and ideas change. This back to the 70's and the style for clothing and how to live life then compared to now. We may find it a little odd, but they found if completely normal.