Weak value amplification is a measurement technique where small quantum mechanical interactions are amplified and manifested macroscopically in the output of a measurement apparatus. It is shown here that the linear nature of weak value amplification provides a straightforward comparative methodology for using the value of a known small interaction to estimate the value of an unknown small interaction. The methodology is illustrated by applying it to quantify the unknown size of an optical Goos-Hänchen shift of a laser beam induced at a glass/gold interface using the known size of the shift at a glass/air interface.