Oh I see. So the thing is that even if ##^4_{R_{i j}}## is of fourth order it doesn't contribute because we see that it is constructed with components of Christoffel's symbol that don't appear in the geodesic equation, so those components aren't measurable, right? I have calculated this...
To anyone who has studied Weinberg's book. Does anyone know why Weinberg discards the fourth order term of the purely spatial components of the ricci tensor? It's the chapter 9 (post-newtonian approximation) of his GR book. It doesn't make sense to me because he includes the R_{00} term of...