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.
They are as you described.
This information enabled BLS to construct the CPI market basket of goods and services and to assign each item in the market basket a weight, or importance, based on total family expenditures. The final stage in the sampling process is the selection of the specific detailed item to be priced in each outlet. This is done in the field, using a method called disaggregation. For example, BLS economic assistants may be directed to price "fresh whole milk." Through the disaggregation process, the economic assistant selects the specific kind of fresh whole milk that will be priced in the outlet over time. By this process, each kind of whole milk is assigned a probability of selection, or weight, based on the amount the store sells. If, for example, Vitamin D homogenized milk in half-gallon containers makes up 70 percent of the sales of whole milk, and the same milk in quart containers accounts for 10 percent of all whole-milk sales, then the half-gallon container will be 7 times as likely to be chosen as the quart container. After probabilities are assigned, one type, brand, and container size of milk is chosen by an objective selection process based on the theory of random sampling. The particular kind of milk that is selected by disaggregation will continue to be priced each month in the same outlet.
In sum, price changes are weighted by the importance of the item in the spending patterns of the appropriate population group. The combination of all these factors gives a weighted measurement of price change for all items in all outlets, in all areas priced for the CPI.