We've already examined the definitions for strong vs. weak acids and bases as they relate to electrolyte behavior. The experimental evidence suggests that there are fewer ions present in aqueous solutions of weak acids or bases than in comparable solutions of strong acids or bases.
One of the first things this should suggest is that we need to be careful with terminology. As we have said before, strong and concentrated (or weak and dilute) have very different meanings. The first term in each pair refers to electrolyte behavior or the tendency to break apart into ions. The second term in each pair refers to Molarity or some other measure of mixture composition.
Another thing which might come to mind when examining weak acids and bases is that their solutions must be equilibrium systems in which the majority molecular species coexists with a relatively small number of ions. Molecules occasionally dissociate into ions and ions occasionally recombine, but the thermodynamics of the situation favor the molecular form.