1 This Psalm commends unto us the mercies of God, proved in ourselves, and is therefore the sweeter to the experienced. And it is a wonder if it can be pleasing to any one, except to him who has learned in his own case, what he hears in this Psalm. Yet was it written not for any one or two, but for the people of God, and set forth that it might know itself therein as in a mirror. Its title needs not now to be treated, for it is Halleluia, and again Halleluia. Which we have a custom of singing at a certain time in our solemnities, after an old tradition of the Church: nor is it without a sacred meaning that we sing it on particular days. Halleluia we sing indeed on certain days, but every day we think it.
For if in this word is signified the praise of God, though not in the mouth of the flesh, yet surely in the mouth of the heart. “His praise shall ever be in my mouth.” But that the title has Halleluia not once only but twice, is not peculiar to this Psalm, but the former also has it so. And as far as appears from its text, that was sung of the people of Israel, but this is sung of the universal Church of God, spread through the whole world. Perchance, it not unfitly has Halleluia twice, because we cry, Abba, Father.
Since Abba is nothing else but Father, yet not without meaning the Apostle said, “in whom we cry, Abba, Father;” but because one wall indeed coming to the Corner Stone cries Abba, but the other, from the other side cries Father; viz., in that Corner Stone, “who is our Peace, who has made both one.”...
Source: The Enarrations, or Expositions, on the Psalms (New Advent)