How to rationalise that when we dilute a weak acid, the pH increases but also the dissociation increases? When water is added to a weak acid like ethanoic acid, the number of ethanoic acid molecules that dissociate increases, however, pH increases (less acidic), too. Why is this so?
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.