I’ll answer your questions in order:
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Yes this is the correct interpretation. I would note that the number of multi-family households is relatively small, and a common practice is to calculate statistics for single-family households only.
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The family weights are currently available as unharmonized variables for the basic monthly samples in IPUMS CPS, called UH_FAMWGT_1 and UH_FAMWGT_2. However these are currently only available up through 2009. IPUMS CPS is planning to add harmonized versions of these weights eventually, but there is currently no timeline for doing so.
These weights are also available for basic monthly samples (for all years) in the original public use microdata files available at NBER. You can merge the variable (called PWFMWGT) from the NBER files into your IPUMS extract using the process described here. -
You’re right that the documentation for this variable is not completely correct, and the family weight is not always equal to the person weight of the reference person. There are adjustments to the weights made to ensure the number of married men equals the number of married women. Unfortunately there is no simple way to calculate the family weights using the person weights. We’ll update this documentation in a future release.
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The post you linked to is not entirely correct. See answers above.