Full Idea
Weak metaphysical necessity is either over the set of all logically possible worlds (in which case it is the same as logical necessity), or it is of a smaller set of worlds, and is determined by the underlying essence or nature of the actual world.
Gist of Idea
Metaphysical necessity can be 'weak' (same as logical) and 'strong' (based on essences)
Source
Robert Hanna (Rationality and Logic [2006], 6.6)
Book Reference
Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.196
A Reaction
I take the first to be of no interest, as I have no interest in a world which is somehow rated as logically possible, but is not naturally possible. The second type should the principle aim of all human cognitive enquiry. The strong version is synthetic.