No, it isn't weird to do that. People do that quite often in many fields.
The long cover letter
is weird and unnecessary.
In my field we do a 1-2 page (1 page is preferable in most cases) cover letter. If you cannot say it in 1-2 pages then the people reading it assume you are longwinded, wordy, and potentially lacking the ability to be clear and concise. Their assumption can be false but that is their first impression. I don't mean to scare you.
