Binding of a dimer of a glycopeptide antibiotic to two molecules of a ligand that are bound to a membrane surface (by a hydrocarbon anchor) has been investigated. This binding on a surface is cooperatively enhanced (surface enhancement) relative to the binding in solution, because the former occurs intramolecularly on a template. Previously a correlation between surface enhancement and thermodynamic stability of the dimer in free solution (K_dim^sol) was hypothesised. However, we found that two weakly dimerising antibiotics (vancomycin and ristocetin A) with similar K_dim^sol give very different surface enhancements. We propose a model to explain the data correlating surface enhancement to the kinetic barrier to dissociation of the dimer. The surface enhancement of binding can be expected to increase with increasing tightness of the non-covalent interactions formed at the dimer interface. The effect should be found in general where cooperativity is exercised within an organised template (e.g., DNA duplexes and proteins).