Depends on what you mean by lightweight. Easy on Ram? Or lighter db file? Or lighter connector to connect to db? Or fewer files over all? I'll give a comparison of what I know:
no of files cumulative size of files db size
Firebird 2.5 5 6.82 MB 250 KB
SqlServerCe 4 7 2.08 MB 64 KB
Sqlite 3.7.11.0 1 0.83 MB 15 KB
VistaDb 4.3.3.34 1 1.04 MB 48 KB
no of files - includes the .net connector and excludes the db file
The dbs are of 1 table with 2 columns and 2 rows. Take the db size with a pinch of salt as dbs could grow differently with further use. For instance SqlServerCe though initially was at 64 KB, it didn't grow at all after adding a few hundred records, while VistaDb grew easily from 48 to 72 to 140 KB. SQLite was the best in that regard which started from the lowest and grew linearly.
Few anecdotes: I had better performance using SqlServerCe with the factory settings which means its the easiest to get kick started without any configuration, while I found Firebird little bit harder to get it started due to lack of online materials. Firebird as I could read had widest standard sql compliance. While VistaDb is written in fully managed C# which means it can be merged with your application's assembly to have one single file, it seemed slowest to me. Of all, considering performance, ease and size I chose SQLite. SqlServerCe would be my second choice.
In short each has its pluses and minuses. Again, take my rant with a pinch of salt, its just my personal experience.
