(To). To sanction, to support. Approval or disapproval is shown by the countenance. The Scripture speaks of “the light of God's countenance,” i.e. the smile of approbation, and to “hide His face” (or countenance) is to manifest displeasure.
“General Grant, neither at this time nor at any other, gave the least countenance to the efforts ...”
—Nicolay and Hay: Abraham Lincoln (vol. ix chap. ii. p. 51).
To keep in countenance. To encourage, or prevent one losing his countenance or feeling dismayed. To keep one's countenance. To refrain from smiling or expressing one's thoughts by the face.
Out of countenance. Ashamed, confounded. With the countenance fallen or cast down. To put one out of countenance is to make one ashamed or disconcerted. To “discountenance” is to set your face against something done or propounded.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894