To Possess force or impact; bring about an effect or an alteration: "Every One Of These elements militated to a different targeting concern” ( Tom Clancy). "The chaste banality of their prose . . . militates up against the stories' becoming literature” ( Anthony Burgess).
which will make war; to fight; to contend; -- typically followed closely by against along with.
to stay conflict or at difference; come into collision.
Hence to face in array; have weight or force, as with determining such a thing: accompanied by against, and permissibly by in favor of: as, these details militate against (or in fovor of) your principle.