Note Pascal has also file of record
file of record is not an acceptable solution either, to many missing parts, TurboPower B-Tree Filer is a far better solution if you want to go down the record route. If I could only find the port posted on the mail list a couple of years back. It did not survived my last disk crash.
FPC has a good lightweight engine as standard: fpindexer. If you want really lightweight
You do know that fpindexer is a full text search engine and not a database, right?
DBase, paradox and the rest of the solutions are not acceptable either the existing components target the file format only, no sql, no network/locks and the index support is sketchy at best. FF2 has the complete package from compressed tables up to encrypted ones with sql support views, stored procedures etc. It is the best pascal database so far and if supported properly it will be far better than sqlite.
As for the popularity of SQLite the main reasons are 1) it is a c based embedded database 2) it is under the BSD license and 3) it has a small footprint. Those reasons makes it a good solution for storage limited devices (mobiles phones, tablets etc). it is not its technical superiority over (firebird for example) other databases that it was chosen.