Is acetate a weak base due to its resonance structure?
Consider this generic acid-base reaction in water:
$$\ce{HA &lt;=&gt;[K_\text{a}] A- + H+ }$$

The (thermodynamic) dissociation constant $K_\text{a}$ depends mainly on two things: 


The stability of the product $\ce{A-}$
The instability of the starting material $\ce{HA}$


The higher one of those factors is, the higher the dissociation constant. So in effect, what a chemist states is the following:

The carboxylate anion is the conjugated base of the carboxylic acid, whose strength is determined by the stability of said carboxylate ion and the instability of the acid. It may be reasoned that carboxylic acids would be much less strong if it was not for the additional stability via conjugation.