How to rationalise that when we dilute a weak acid, the pH increases but also the dissociation increases?
It's simply due to dilution. 

If it's true that adding water increases dissociation (Gerard has done a nice effort in Does the number of H+ ions in solution go up on dilution of a weak acid?), concentration of $\ce{H3O+}$ inevitably decreases. As a consequence, $\mathrm{pH}$, defined as $-\log[\ce{H3O+}]$, increases.

Start with $\pu{1 L}$ acetic acid concentration $\pu{1 M}$,
$$\ce{[H3O+]} = \sqrt{K_c} = \pu{4.22E-3M},$$
that corresponds to $\pu{4.22E-3mol}$ of $\ce{H3O+}$.
If you double the volume ($\pu{2 L}$),
$$\ce{[H3O+]}=\sqrt{K_c/2}=\pu{2.98E-3M},$$
that corresponds to $\pu{5.96E-3mol}$ of $\ce{H3O+}$.

The amount of substance is higher, but concentration is less: dilution does play a role here.