Will SQLite performance degrade if the database size is greater than 2 gigabytes?
Usually the larger the database the more data you have in it. The more data you have, the longer searches may take. They don't have to, it depends on a search.
As for inserts, they may take longer if you have many indexes on a table. Rebuilding an index may take some time, so expect insert speed degradation with the amount of data.
Updates may also be slower - fitting rows must be found first (search), then values have to be changed (may trigger an index rebuild).
I am telling you this from experience: if you expect a lot of data in your database, consider splitting it into multiple databases. This works if your data is gathered daily and you can create a database for each day. May make your search code more complex, but will speed things up for limited searches/
There is no 2 GB limit.
SQLite database files have a maximum size of about 140 TB.
On a phone, the size of the storage (a few GB) will limit your database file size, while the memory size will limit how much data you can retrieve from a query. Furthermore, Android cursors have a limit of 1 MB for the results.
The database size will, by itself, not affect your performance. Your queries will be fast as long as they do not access more data than fits into the DB's page cache (2 MB by default).