When analyzing food security supplement data that includes the food security scores, the appropriate weight to use is FSHWTSCALE. As you can see on that variable’s description page, this is generally identical to the standard food security supplement weight, FSSUPPWTH, except in 1998, 1999, and 2007. All of the weights in IPUMS CPS are sampling weights; in Stata these are pweights (see the Stata weight guidance for more information). I would also note that if you are analyzing data at the household level, you’ll want to restrict your sample to only one person per households using a condition such as “if pernum==1”.
While using FSHWTSCALE will get you the correct point estimates, since the CPS is a stratified cluster sample you need information on strata and cluster in order to get accurate estimates of standard errors. Unfortunately, there are no sampling design variables available in the CPS public use microdata, so you can’t specify exact strata or clusters using svyset. Additionally, while the Census Bureau offers replicate weights for the supplement microdata in recent years, these are not yet available through IPUMS CPS. Replicate weights allow researchers to obtain more accurate estimates of standard errors because they incorporate information on the sampling design.
Given these limitations, I can give you two suggestions for how to obtain standard errors that are more accurate than simply using FSCHWTSCALE and ignoring the stratified cluster sampling design:
First, while the replicate weights are not yet available directly through IPUMS (except for ASEC samples), you can add the weights to your IPUMS extract using the process described at this thread. You can download the replicate weights for supplements from the Census Bureau website. You can find information on how to use replicate weights in IPUMS CPS at this page. That page is specifically about the ASEC, but the same procedure applies to replicate weights from other supplements.
Second, there has been some research showing that using the lowest level of geography available as the strata and using household as the cluster can improve your estimates of standard errors. See Davern et al. (2006, 2007) in the journal Inquiry for more details.