What's happening at the beginning of a weak acid titration?
Unfortunately this is not correct. 


  $$\ce{CH3COOH~(aq) + H2O(~l) &lt;=&gt; CH3COO- ~(aq) + H3O+~(aq)}$$


If you have a pure acetic acid solution the equation you state governs the pH of the solution.

If you are now adding a strong base like $\ce{{}^{-}OH}$, you are removing the hydronium ion from the right hand side of the equation. According to Le Châtelier, the equilibrium adapts and shifts more to the right, i.e. more acetic acid dissociates. As you remove $\ce{H3O+}$ the pH increases.
Another way of looking at this is, that you remove acetic acid from the left hand side (similar to what you stated).
$$\ce{H3CCOOH + {}^{-}OH &lt;=&gt; H3CCOO- + H2O}$$
According to Le Châtelier, the equilibrium (in the first equation) has to shift to the left, to regenerate more acetic acid, removing once again $\ce{H3O+}$ and the pH increases. 

In any case you choose to look at, you increase the concentration of acetate in the solution and another equilibrium comes into play.
$$\ce{H3CCOO- + H2O &lt;=&gt; H3CCOOH + {}^{-}OH}$$
This equilibrium is essentially responsible for raising the pH.