The strength of the acid, HA, depends SOLELY on the extent this equilibrium lies to the right.
Strong acids, HX (X!=F), HNO_3, H_2SO_4, HClO_4, undergo almost complete ionization, and 1*mol*L^-1 solution of such acid is stoichiometric in H_3O^+ and X^- (what does "stoichiometric" mean in this context)?
On the other hands, for weaker acids such as "acetic acid", "phosphoric acid", "carbonic acid", the equilibrium lies towards the reactants as written, and at equilibrium significant concentrations of HX obtain. This is a very important definition, so please try to get it right.
So to finally answer your question: the conjugate base of a weak acid competes strongly for the proton, and at equilibrium, appreciable concentrations of HA obtain.
"Claro?"
