Cynical take: Because the people in power defining the inflation calculations don't want people to realize they're being fleeced.

Rent and health insurance are included in CPI.

And they use BS games to minimize the increases - things like equivalency pricing. My health insurance hasn't gone up that much in the last 5 years on per month basic. The difference is instead of the $10 copay on day 1 that I used to have, I now have a $3K deductible and my in-network choices have been cut in half.

I'm guessing there are similar games done with housing. For example, prices for condos in a lot of areas have probably kept pace with inflation, but meanwhile the HOAs have gone up from $200/month 10 years ago to $400/month now, and I suspect it's because government services have been cut. I doubt the fed takes into consideration things like my area is now so crowded, I pay $100/month to park whereas 10 years ago it was free. Same with tolls - the once free interstates have all been converted to toll roads in my area that cost $40/week to get to work.

But how much weight are they given?

I will forever fail to understand why commenters on hacker news ask questions for which the answer is public and readily available. I think it's because they think that the answer to the question will favor them and the idea is that astute readers will do research and thus be convinced of the commenter's point.

Unfortunately, in this case, an astute reader would do research and conclude that the point you are trying to make is completely mythical. Housing (total, rent + everything else) accounts for 42% of the CPI calculation, and the 'owners equivalent of rent' (i.e. how much you would have to pay to rent your home) makes up ~24%: https://www.bls.gov/cpi/tables/relative-importance/2016.pdf

That captures rent renters pay as well, since for apartment buildings, the owner's equivalent rent is the rent being paid.

In PCE (Personal Consumption Expenditures), it's weighted half as much. Is the median person really paying only 12.9% (or 15.3%) of their income for rent? Seems like it's usually closer to 30-40%, and sometimes higher for the working class. (12.9%-15.3% of median household income is only ~$7740-9180 which would be only $645-765/mo.)

That one at least weights medical care at 22.3% ($13380) vs the 6.2% ($3700) in CPI, although that might be realistic if the median person simply doesn't get medical care because they can't afford it.