Summary: For lattice models on \(\mathbb{Z}^d\), weak mixing is the property that the influence of the boundary condition on a finite region decays exponentially with distance from that region. For a wide class of models on \(\mathbb{Z}^2\), including all finite range models, we show that weak mixing is a consequence of Gibbs uniqueness, exponential decay of an appropriate form of connectivity, and a natural coupling property. In particular, on \(\mathbb{Z}^2\), the Fortuin-Kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially, and the \(q\)-state Potts model above the critical temperature is weak mixing whenever correlations decay exponentially, a hypothesis satisfied if \(q\) is sufficiently large. Ratio weak mixing is the property that uniformly over events \(A\) and \(B\) occurring on subsets \(\Lambda\) and \(\Gamma\), respectively, of the lattice, \(| P(A\cap B)/P (A)P(B) -1|\) decreases exponentially in the distance between \(\Lambda\) and \(\Gamma\). We show that under mild hypotheses, for example finite range, weak mixing implies ratio weak mixing.