I agree with others on here. It's only weird if you think it's weird.
First time I went by myself was for my 30th birthday. I was meeting a friend in L.A. for a golf weekend and got there a day early so I decided to spend a day in the park. I hadn't been there in 13 years and was really looking forward to seeing what was new and revisit old memories from my childhood. The 50th celebration was still going on, so I got myself a happy birthday sticker (they either hadn't started the birthday buttons yet or were out of them), a pair of golden Mickey ears and hit it. For me, It felt like having the whole park to yourself. You can go where you want to, when you want to. I chatted up people in line from time to time, hit all my favorite rides and ones that were newer than my previous trip (Like Indiana Jones). I didn't realize it at the time but it was also the very last day that POTC was open before being closed for adding the Captain Jack theme. Being my favorite attraction, it's a cool thought that I was one of the very last people who got to experience the (mostly) original version of POTC.
The only time it felt weird was standing in line for Alice in Wonderland. I was the only single adult male in that queue and I started wondering to myself how creepy this might appear to the families in line with me. lol It was all in my own head though and I quickly got over it.
Only recommendation I would have is to take your time. Having been so long since I had been there, not having a group to slow me down some and the fact that it was only for one day, I think I rushed myself through too fast in order to squeeze as much as possible into that day. I've come to realize that I enjoy the park better at a leisurely pace and having something to look forward to for next time helps keep it fresh for me.