A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 56:1Upon Jonath-elem-rechokim--literally, "upon the dove of silence" of distant places; either denoting a melody (see on Psa 9:1) of that name, to which this Psalm was to be performed; or it is an enigmatical form of denoting the subject, as given in the history referred to (Sa1 21:11, &c.), David being regarded as an uncomplaining, meek dove, driven from his native home to wander in exile. Beset by domestic and foreign foes, David appeals confidently to God, recites his complaints, and closes with joyful and assured anticipations of God's continued help. (Psa 56:1-13)
would swallow--literally, "pants as a raging beast" (Act 9:1).
psa 56:2enemies--watchers (Psa 54:5).
most High--As it is not elsewhere used absolutely for God, some render the word here, arrogantly, or proudly, as qualifying "those who fight," &c.
psa 56:3in--or literally, "unto."
thee--to whom he turns in trouble.
psa 56:4in God . . . his word--By His grace or aid (Psa 60:12; Psa 108:13), or, "I will boast in God as to His word"; in either case His word is the special matter and cause of praise.
flesh--for mankind (Psa 65:2; Isa 31:3), intimating frailty.
psa 56:5A vivid picture of the conduct of malicious enemies.
psa 56:7Shall they escape? &c.--or better, "Their escape is by iniquity."
cast . . . people--humble those who so proudly oppose Thy servant.
psa 56:8God is mindful of his exile and remembers his tears. The custom of bottling the tears of mourners as a memorial, which has existed in some Eastern nations, may explain the figure.
psa 56:9God is for me--or, "on my side" (Psa 118:6; Psa 124:1-2); hence he is sure of the repulse of his foes.
psa 56:12I will render praises--will pay what I have vowed.
psa 56:13The question implies an affirmative answer, drawn from past experience.
falling--as from a precipice.
before God--in His favor during life.