That means there is a very small amount of H⁺ present at all times. These hydrogen ions are strongly attracted to acetate ions--that is why acetic acid is a weak acid. So when these ions encounter one another in solution they will likely recombine:
CH₃COO^-(aq) + H⁺(aq)

CH₃COOH(aq) This equilibrium favors the product (remember, the acid is weak). But as H⁺ ions are gobbled up by the acetate ions, the equilibrium in water is affected. In order to restore equilibrium, more water molecules must dissociate:

H₂O(ℓ)

H⁺(aq) + OH^-(aq)

The result is a small excess of OH^- in the mixture. It's basic! A similar argument can be used to show why solutions of weak base cations are acidic but it's a stretch without resorting to Brønsted .