I've noticed using BackupLoupe that stuff under
~/Library/Saved Application State/ pops up in my Time Machine backups. I can't find that much about this folder online, but one site describes it as "where the information regarding files that should be re-opened on startup is stored." This doesn't sound to me like it needs to be covered by Time Machine backups. Is there a good reason why this folder needs to be backed up?
The folder is small, but if it changes frequently then its footprint in Time Machine could be large.