While the family weight is not available as its own variable in IPUMS CPS, you could construct the appropriate family weight by assigning the ASECWT of the first person in every family to the family weight. Using just the 2016 ASEC data, you could use the following code to accomplish this:
bysort serial famid (pernum): gen fpernum=_n
gen famwt=asecwt if fpernum==1