Re-evaluation of Consumer Price Index (C.P.I.) weights How are the weights of the various household items in the Consumer Price Index (C.P.I.) basket decided, i.e., how are they re-evaluated every year? Is it done manually or automatically?  

If its done manually, then how can they be sure (i.e., what methods, statistical or mathematical) that the weights represent the general average consumption of that item in the household? Else, if  its done automatically, then what is the strategy (i.e., what sort of algorithms or data structures) used to ensure the accuracy of the weights.
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
  2-week period.
  
  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
  sources.


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.