In general, you should use the most restrictive weight for variables included in your analysis, regardless of whether or not those variables are your outcome measure. FSSUPPWT and FSSUPPWTH are the appropriate person- and household-level weights for analyzing food security supplement (FSS) data as these are more restrictive than WTFINL. This is particularly true if you plan on restricting the sample based on FSFDSTMP. If you’re analyzing one of the food security scale variables, then you should use FSHWTSCALE as your weight instead. Additionally, each month, the CPS includes a sub-set of questions asked of the outgoing rotation groups (ORGs). These questions are often called the Earner Study. For analyses that use ORG questions, EARNWT is generally appropriate as it is more restrictive than the FSS weights. Note that this all assumes you are only using data from December; weighting guidance for linking FSS variables to outcomes in other months of the survey is less clear cut.
Hope that helps.