CPI is a weighted index of price changes. So what are the weights? These are available from the BLS website using the keywords "relative importance of components in the consumer price index". Here's the page.
Do note the indents, they're important: all items at the same level of indent add up to the total percentage of the category. For example, the category "All Items" is 100% of the CPI. But this can be broken down into components with the next leftmost indent: Food and Beverages, Housing, Apparel, Transportation, Medical, Recreation, Education and Communication, and Other Goods and Services.
In turn, some of those get broken down even further. So, Breakfast Cereal is a component of Cereals and Cereal Products, which is part of Cereal and Bakery Products, which is part of Food At Home, which is part of Food, which is part of Food and Beverages.
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There are price indices for all of those components. But it can be difficult to find them all in one place. FRED has this page which shows some before and after indices and base years for components of the CPI down to the 5th indent level (and some at the 6th). However, the amount of data underlying this table is huge, so you can't just go an download everything easily.
Anyway, I put this into a spreadsheet which you can find in the class shared folder on Google Drive.
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