We present an in situ investigation of the correlation between elastic and magnetic properties of monolayer iron films on W(110). Sesquilayers, consisting of two-monolayer patches on a nearly ideal monolayer film, exhibit anomalous elastic properties and a strikingly high in-plane coercivity of order 0.3 T. The sesquilayer coercivity maximum is explained by a novel domain wall pinning mechanism, based on an enhanced exchange interaction in the two monolayer thick patches. This rather unique behavior is restricted to (110) surfaces but does not occur on (100) and (111) thin films.