As stated in Hennig et al. 2016 Handbook of cluster analysis:
If for subject matter reasons some variables are more important than others regardless of the within-variable variation, one could reweight them by multiplying them with constants reflecting the relative importance after having standardized their data-driven impact.
I feel that this is related to my data which I want to cluster using K-medoids algorithm, but I don't know the exact relationship between variables, i.e. I know that $var2$ should be more important than $var1$, but it is unknown if $var2$ is twice much important as $var1$ or maybe threefold, or even fourfold. Is there any established method or a measure to assess what should be the value of this weight other than an eye-test?