I guess you can say I just don't understand the mesomeric effect
That's the first step to improvement;)
let's recap:
Acid/Base Questions are all about Equilibrium, which is all about Thermodynamics. We look at an acid and it's conjugated base. To understand this equilibrium, you have to look at both sides of the equation. The acidity is determined by the energy difference of the acid and the conjugated base. So:
if you stabilize the protonated form, you make the molecule less acidic.
if you destabilize the protonated form, you make the molecule more acidic.
if you stabilize the deprotonated form (the conjugated base), you make the molecule more acidic.
if you destabilze the deprotonated form, you make the molecule more acidic.
usually, one of the latter two is explaining these kind of questions.
Now further. What do we mean by "mesomeric effect". To put it simple: usually after deprotonation, the conjugated base carries a negative charge, and charge separation means higher energy. If the molecule is able to distribute this charge over several atoms, we can assume that this stabilizing. how do we know if the molecule can distribute/delocalize this negative charge? We draw all the sensible lewis structure, all resonance structures. do you know how to do that? do you see the difference between RCOOH and ROH?
"Inductive effects" are usually not that strong. But some groups can "pull or push" electron density. Pulling electrons from the negative charge is stabilizing. and vice versa.
the first molecule is less acidic than the reference. The difference between the molecules is a -CH3 bond, which is supposed to be a inductive donor and therefore it unstabilizes the conjugate base? Is this right?
yes, alkylgroups are inductive donors.
(it's always like that in OC (for me), there are concepts which seem to work quite well. but after all, you have to have seen it somewhere to really know;))