How much does adding an opening book to a relatively weak chess program affect its strength? Jonathan Schaeffer in One Jump Ahead (via the Chess Programming Wiki):

To solve the opening problems of his chess machine, Belle, Ken
Thompson typed in opening lines from the Encyclopedia of Chess
Openings (in five thick volumes). Religiously, he dedicated one hour a
day for almost three years (!) to the tedious pursuit of entering
lines of play from the books and having his Belle computer verify
them. The result was an opening library of roughly three-hundred
thousand moves. The results were immediate and obvious: Belle became a
much stronger chess program, and Ken probably aged prematurely.

I read somewhere else that Belle eventually reached the equivalent of 2250 Elo (I assume that was in terms of USCF ratings), but I couldn't find any information about its rating gain due to the opening book.
So here's a more general question. Suppose we take a relatively weak chess engine that doesn't use an opening book and that has a known rating from a pool that includes humans (e.g. Lichess or chess.com). How much stronger would it be if we added an extensive opening book to it?
Let's assume the engine's original rating is anything between the equivalent of 1000 to 2000 FIDE. This is an arbitrary range. The idea is that if the engine is too weak, then the opening book would be just covering for the lack of any search/evaluation, and if it's too strong then the opening book would get less necessary. Of course I expect the answer to be different depending on the strength of the original engine.
Stockfish gains about 50 elo from the Cerebellum opening book (&quot;Brainfish&quot; is just Stockfish equipped with Cerebellum).
I don't know if the effect of opening books varies depending on engine strength, however.