Leaving group ability is tied to the stability of the leaving group. Acidity is directly related to the stability of the conjugate base. If you're a strong acid, the conjugate base is relatively stable in solution. Less so, if you're a weak acid. So the stability of the conjugate base is directly proportional to both acidity and leaving group ability.
Edit:
$$\ce{HA->H+ + A-}$$
$\ce{A-}$ is the species we're evaluating as the leaving group. Basically, it's a good leaving group if it's stabilized. If that's the case, the acid dissociation equilibrium also shifts toward products, making $\ce{HA}$ a stronger acid. You should be careful to differentiate between $\ce{HA}$ and $\ce{A-}$ when you're thinking about these concepts.