My take on this: It doesn't really matter what other people think, what matters is what you think. So if you're afraid of getting weird looks and are kind of expecting them, you might see them even when they aren't really there. The trick is trying to not care so much, even though I know it's easier said than done - remind yourself that you most likely won't see any of the others ever again and you should not allow them to have any power over whether you enjoy the experience or not.

It's not like a party or something - sitting in the dark watching a movie is a pretty solitary thing to do anyway; even the people who don't go to the movies alone will hardly interact with each other during the movie, unless they're noisy and inconsiderate. So someone sitting alone enjoying the movie all by themselves should not be considered as weird, and if anything, people might even appreciate that you're not one of the loudly talking and laughing spectators causing distractions.

I do go to movies alone when I can't find noone else to accompany me. I don't think it's weird. I do feel a bit awkward though before the movie starts, if I just sit there alone, waiting, so I prefer to distract myself by studying movie posters / description (while still in the foyer) or reading something / playing around with my phone / listening to music on headphones while seated, until there are images on the screen. The other spectators usually will pay no attention to you though if you don't stare into their direction constantly, wondering what they would think about you. They don't really care. Buying 3 tickets just so noone can take a seat next to you seems a bit extreme to me, but then again, I don't know how it's like for you. Do you get panic attacks being so close to other people?

In any case, I would suggest to wait a couple of weeks after release, especially with such a blockbuster, so you can expect less crowded halls, and maybe it's also better to go to really late night screenings on week days rather than earlier ones (e.g. 11 pm would probably be less crowded than 6 pm, I assume; though if there are screenings in the morning, at noon or during the early afternoon, that might be even better - though the latter comes with the risk of more kids, if that bothers you).