As a followup, when I created the second layer I used
v.db.connect map=baseMap driver=sqlite table=CountyData key=FIPS layer=2
There is a column in baseMap called FIPS but it is not the category data. Is the link with the attribute table from layer 1 automatic? Do I need to create a cat field in CountyData? If I do, how to I link it with the FIPS column in baseMap?
Because of the possibility that there are multiple vector regions for a county in baseMap, there are many cases of repeated values for the FIPS data, but they are unique in CountyData.
Could another possibility be in how I imported the data into SQLite? I used a straight forward db.copy of a DBF file.
This is Grass 6.3 on OS X. I read that there was a problem with labeling on layer 1 with 6.2, but is the same type problem?