“In David we have a notable example of a sensitive, tender, self analysing soul, living in sustained communion with God, while deeply sensible of the claims of the civil and religious polity of Israel, and, moreover, while externally devoted to a large round of exacting public duties. And in this Psalm public misfortunes do but force him back upon the central strength of the life of his spirit. For the time his crown, his palace, his honours, the hearts of his people, the love of his child, whom he loved, as we know, with such passing tenderness, are forfeited. The psalmist is alone with God. In his hour of desolation he looks up from the desert to heaven. O God, he cried, thou art my God. In the original language he does not repeat the word which is translated God. In Elohim,the true idea of the root is that of awe, while the adjectival form implies permanency. In Eli, the second word employed, the etymological idea is that of might, strength. We might paraphrase, “O thou Ever awful One, my Strength, or my Strong God art thou.” But the second word, Eli, is in itself nothing less than a separate revelation of an entire aspect of the Being of God. It is, indeed, used as a proper and distinct name of God. The pronomial suffixes for the second and third persons are, as Gesenius has remarked, never once found with this name El;whereas Eli, the first person, occurs very frequently in the Psalter alone. We all of us remember it in the words actually uttered by our Lord upon the cross, and which he took from their Syriacised version of Psalm 22. The word unveils a truth unknown beyond the precincts of revelation. It teaches us that the Almighty and Eternal gives himself in the fulness of his Being to the soul that seeks him. Heathenism, indeed, in its cultus of domestic and local deities, of its penates, of its Oeoi epicwrioi, bore witness by these superstitions to the deep yearning of the human heart for the individualizing love of a higher power. To know the true God was to know that such a craving was satisfied. My God. The word represents not a human impression, or desire, or conceit, but an aspect, a truth, a necessity of the divine nature. Man can, indeed, give himself by halves; he can bestow a little of his thought, of his heart, of his endeavour, upon his brother man. In other words, man can be imperfect in his acts as he is imperfect and finite in his nature. But when God, the Perfect Being, loves the creature of his hand, he cannot thus divide his love. He must perforce love with the whole directness, and strength, and intensity of his Being; for he is God, and therefore incapable of partial and imperfect action. He must give himself to the single soul with as absolute a completeness as if there were no other being besides it, and, on his side, man knows that this gift of himself by God is thus entire; and in no narrow spirit of ambitious egotism, but as grasping and representing the literal fact, he cries, “My God.” Therefore does this word enter so largely into the composition of Hebrew names. Men loved to dwell upon that wondrous relation of the Creator to their personal life which is so strikingly manifested. Therefore, when God had “so loved the world, that he gave his only begotten Son, that whosoever believeth in him shall not perish, but have everlasting life, “we find St. Paul writing to the Galatians as if his own single soul had been redeemed by the sacrifice of Calvary: “He loved me, and gave himself for me.””
– Henry Parry Liddon, in “Some Words for God: being Sermons preached before the University of Oxford, 1863-1865.”

http://www.spurgeon.org/treasury/ps063.php