Favor, countenance, encourage are comparable when they mean to give the support of one’s approval to.
Favor may be used in reference to a well-disposed inclination, an expressed preference, or active support or sometimes to a circumstance or agency conducive to a result.
Countenance may indicate mere toleration; more often it implies a positive favoring.
Encourage carries the notion of heartening stimulation, inciting or inducing especially by expressions of approval, confidence, liking, or comfort.