I don't know if there's any way to know if it would be "weird" or not since you wouldn't get a response. I would do what was helpful to me. It is just a letter, he can choose to open it/read it or not so no boundaries are being crossed. I've e-mailed former professors to tell them how much their class helped me a year or more after I took it, I think a letter to a former therapist/pdoc is similar. I wrote my therapist occasionally for a year or two after I terminated with her back in the 1980's and then was able to see her again in the mid-90's. I think such a question can only be answered by you and what will help you/make you feel better as the other person doesn't really "exist" since there's no feedback. If it were "bothersome" in some way; if you mailed a letter every day or something, that would be different.