There is more helpful information in the WTSUPP description that I believe also applies to the WTFINL variable:
"Estimates on the entire population are prepared by projecting forward the resident population from the last available census. These projections are derived by updating the demographic census data from a number of other data sources that account for death, births and net migration. About 3 years after every census (i.e. 2003 for the 2000 Census and 2013 for the 2010 Census), the Census Bureau updates its independent population control and provides a new weight for the relevant years.
Two important points should be noted here. First, the lag between when the Census is conducted and when the CPS weights are updated is about 3 years. While the Census data are being processed, the CPS files are made available using the weighting scheme from the US Census prior to the latest Census. Second, once the files are updated, the old weights become obsolete and are replaced in the IPUMS data extract system. Published estimates from the lag years that use the old weights are not always updated. For example, 2010 poverty estimates were released in ASEC using the 2000 population controls. Once the 2010 population controls were made available, IPUMS-CPS replaced the ASEC 2010, 2011, and 2012 weights that are based on the 2000 population control with weights that are based on the 2010 population controls. IPUMS-CPS makes available only the most up-to-date weights."
The takeaway here is that (I believe) these weights are adjusted–and updated retroactively–based on each decennial Census. They then carry through these weights until the next Census, when you see another discrete jump.