Is it weird writing a teacher appreciation letter?
Yes she would appreciate a letter of gratitude from you as it would make her job as a teacher being worthwhile.
She will, no doubt, be surprised to receive your letter, but I am sure that she will also be pleased that you have taken the trouble to write it. I don't think that it would be a weird (I suppose that you mean 'strange') thing to do. Most people like to know that their efforts have been appreciated. Keep the letter short. Wordiness would not be welcomed. You should assume that she does not remember you, so don't go on at some length. Be polite, keep it short, and your letter will be well received. And I hope that you have a good day, also.
No, it would be an honor to receive such a letter from a student!