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?"#
