The Collaborative International Dictionary of English v.0.48:
Militate \Mil"i*tate\, v. i. [imp. & p. p. Militated; p. pr. &
vb. n. Militating.] [L. militare, militatum, to be a
soldier, fr. miles, militis, soldier.]
To make war; to fight; to contend; -- usually followed by
against and with.
[1913 Webster]
These are great questions, where great names militate
against each other. --Burke.
[1913 Webster]
The invisible powers of heaven seemed to militate on
the side of the pious emperor. --Gibbon.
[1913 Webster]