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 121:1God's guardian care of His people celebrated. (Psa 121:1-8)
I will lift up mine eyes--expresses desire (compare Psa 25:1), mingled with expectation. The last clause, read as a question, is answered,
psa 121:2by avowing God to be the helper, of whose ability His creative power is a pledge (Psa 115:15), to which,
psa 121:3His sleepless vigilance is added.
to be moved--(Compare Psa 38:16; Psa 66:9).
psa 121:5upon thy right hand--a protector's place (Psa 109:31; Psa 110:5).
psa 121:6God keeps His people at all times and in all perils.
nor the moon by night--poetically represents the dangers of the night, over which the moon presides (Gen 1:16).
psa 121:8thy going out, &c.--all thy ways (Deu 28:19; Psa 104:23).
evermore--includes a future state.