Is it weird for a female who is 26 or 27 to date a guy who is 20 going on 21?
It depends on where they are in their lives (at least for long-term relationships). I dated my ex when I was 19 and she was 25. We got along well, sex was great, etc. The problem was that she was ready to settle down. Me (being 19 and halfway through college at the time) thought it'd just fine to potentially marry her. She thought otherwise and ended it.
I didn't realize until later that she saved me from a life time of hating myself and her. She's engaged now (a little less than a year after we broke up), and I'm 100% grateful she knew that it wouldn't have been fair for her to take away the rest of my college/early adult years by committing me to her and a future family.