If you look closely at your diagram, you will notice that once benzoic acid has released its proton, the conjugate base that is formed has 6 resonance structures out of which 4 have 2 more charges that offset each other. The overall charge of benzoate anion is -1 regardless.
The important part of this discussion revolves around the last 4 resonance structures. For the sake of the discussion, I will only refer to the 2 charges that offset each other. When a negative charge appears on the oxygen atom in the carboxyl group, a positive charge appears on the ring (the charge is spread across the nucleus).
At this point, we see that the conjugate base is quite stable because it has 6 resonance structures. The more resonance structures the conjugate base has, the stronger the acid is. This is how the acidity of benzoic acid is explained.
Now, if you placed a methoxy group in para position, it would doante electrons to the ring through a mesomeric effect. If that happens, the electron density around the nucleus increases, diminishing the positive charge. The methoxy group increases the electron density and so the positive charge on the nucleus is no longer “that positive” while the negative charge remains unaffected (“just as negative”). If the positive charge can’t properly balance the negative charge, the resonance structures involving charge separation are not advantageous to exist and so the strength of the acid decreases.
This happens only if the methoxy group is situated para relative to the carboxyl group. If it is situated meta relative to the carboxyl, something interesting happens.
We know that the methoxy (like the hydroxy group) exerts a -I inductive effect and a mesomeric (M) effect. That is why, if found para, it “donates” electron density through a +M effect (which manifests more than -I). When in meta, the +M effect is no longer a dominant effect and so, methoxy manifests -I effect mostly, withdrawing electron density from the nucleus. It is often said that hydroxy and methoxy groups are EDG, but only when it comes to electromeric effects. They also have -I inductive effects which makes them EWG.
Overall, the presence of a EDG in ortho or para destabilises the actual negative charge of the benzoate anion, thus making it less stable.