My hat theory lol. 😂
The loss of his hat is significant..and the fact Liz keeps wearing a similar one to him from the moment he first sees her is also significant..her character didn't need a hat at all so it could symbolise something else. the hat stands out when she wears it..its meant to canth the audiences eye. In my opinion its no coincidence that Jack's character is missing his hat throughout the movie and Liz's charcter is basically wearing it.its like a puzzle piece thats meant to fit together.
So basically to start with he's loses his beloved hat and it makes him feel incomplete. He wants it back to make him feel complete
The part in Tortuga where he didn't feel right trying on all the hats has a double meaning. Its also the point in the movie where his character is in a great state of confusion over what the compass is telling him he wants..he thinks its saying lots of different things (when its actually pointing to liz) He leaves with no hat..he didn't find the right one.
Then hello hello... Liz turning up looking like him but wearing a hat similar to his missing one symbolises that SHE is the missing part of him.
notice he stops thinking about the hat after he meets her.
At the end after he gets what he wants from Liz strangley enough his hat comes back symbolises that he's finally found the missing part of himeslf "coincidently" when LIZ just came down to his level
muahahahah
hidden meanings everywhere.
This film is massivly based around little "coincidences" that have a much deeper meaning.