[thackney]

but they give them very little weight

They are weighted by average consumer expenditures.

Nonessential and luxury items should be removed from the CPI

The CPI should reflect the average consumers expenditures, not be restricted to the bare essentials.

[Beagle8U]

“They are weighted by average consumer expenditures.”

They should be weighted by % of average consumer expenditures. If based on that, food, energy, transportation, housing,clothing, and health care would be the vast majority of the CPI.