I guess it all depends on your usage pattern. If you use WeeWX the normal way: writes are done by the main thread, while the reporting threads do only reads, it should not be a problem. Right now, many RESTful threads often read the same database file, indeed, the same database table, simultaneously without problem.
OTOH, if you try to write from something other than the main thread, then you might get contention. Both the main thread and your thread could be seeking EXCLUSIVE locks, leading to writer starvation.
-tk