I don't think they are "sure", but the weights are based on the American Consumer Expenditure Survey which has a big sample size, a carefully chosen sampling frame, professionally executed sample gathering, and a large team of experts crafting questions and collating the data.
How is the CPI market basket determined?
The CPI market basket is developed from detailed expenditure
information provided by families and individuals on what they actually
bought. For the current CPI, this information was collected from the
Consumer Expenditure Surveys for 2011 and 2012. In each of those
years, about 7,000 families from around the country provided
information each quarter on their spending habits in the interview
survey. To collect information on frequently purchased items, such as
food and personal care products, another 7,000 families in each of
these years kept diaries listing everything they bought during a
Over the 2 year period, then, expenditure information came from
approximately 28,000 weekly diaries and 60,000 quarterly interviews
used to determine the importance, or weight, of the more than 200 item
categories in the CPI index structure.
Consumer Price Index Frequently Asked Questions (FAQs)
Consumer expenditure data supplied by the CE Survey are a critical
component of the CPI, as they are used to estimate weights for the
CPI’s consumer goods and services classification structure used in the
calculation of the CPI. In the construction of the CPI, four distinct
functional uses of CE Survey data are made: (1) to estimate biennial
expenditure weights, (2) to estimate monthly expenditure weights, (3)
to calculate the probability that an item’s price will be included in
the CPI calculations, and (4) to allocate expenditure estimates
between more-broadly defined expenditure categories from other survey
Research highlights of the Consumer Expenditure Survey redesign
Page 6 of BLS Handbook of Methods, April 1997, Chapter 16: Consumer Expenditures and Income has a nice, detailed description of how "The estimation of population quantities of interest, such as the average expenditure per consumer unit on a particular
item category, is achieved through the use of weights." Be sure to check that out too.