Always believed that on an R22 it was to do with CoG in relation to fuel.
Think you'll find that as the main fuel tank is located on the left hand side that pilot and fuel weight would cause CoG problems and insufficient cyclic control movement to maintain any sort of hover. Figured that was also why the PoH specifies a minimum pilot weight as well as maximum seat and baggage weights.
Presume similar reasons for the R44 and 206. All naturally hover left skid low so better distribution of weight must help. However willing to be enlightened by those more in the know.