The response to strain in covalently bound single layers has a large impact on the growth and properties. We investigate the quasi-two-dimensional hexagonal boron nitride on Rh(111), which is interesting due to its high intrinsic corrugation. We use combined atomic force and scanning tunneling microscopy to measure the response of this monolayer to probing forces. Three-dimensional force maps and the atomic resolution of the layer enable us to determine lateral and vertical stiffness of this prototypical system with unprecedented spatial resolution. Extremely low stiffnesses approximate to 1 N/m are derived. Our experiments give insights into the mechanical properties of corrugated incommensurate layers that buckle into the third dimension to relieve strain.