Enhancers control the location and timing of gene expression and contain the majority of variants associated with disease^1-3. The ZRS is arguably the most well-studied vertebrate enhancer and mediates the expression of Shh in the developing limb⁴. Thirty-one human single-nucleotide variants (SNVs) within the ZRS are associated with polydactyly^4-6. However, how this enhancer encodes tissue-specific activity, and the mechanisms by which SNVs alter the number of digits, are poorly understood. Here we show that the ETS sites within the ZRS are low affinity, and identify a functional ETS site, ETS-A, with extremely low affinity. Two human SNVs and a synthetic variant optimize the binding affinity of ETS-A subtly from 15% to around 25% relative to the strongest ETS binding sequence, and cause polydactyly with the same penetrance and severity. A greater increase in affinity results in phenotypes that are more penetrant and more severe. Affinity-optimizing SNVs in other ETS sites in the ZRS, as well as in ETS, interferon regulatory factor (IRF), HOX and activator protein 1 (AP-1) sites within a wide variety of enhancers, cause gain-of-function gene expression. The prevalence of binding sites with suboptimal affinity in enhancers creates a vulnerability in genomes whereby SNVs that optimize affinity, even slightly, can be pathogenic. Searching for affinity-optimizing SNVs in genomes could provide a mechanistic approach to identify causal variants that underlie enhanceropathies.