What makes you believe that housing is not included? Consider using a search engine (Google is pretty good) and using keywords like "cpi shelter weight" or "cpi housing weight". The BLS has a page on the subject.
My apologies for not knowing offhand everything that goes into the CPI, and not googling it for more context, I was just asking questions on the internet instead. I should've known better than to hope for learning something from my fellow humans.