My thesis is that in the Scripture when God "blesses" men they are thereby helped and strengthened and made better off than they were before, but when men "bless" God he is not helped or strengthened or made better off. Rather (with C. A. Keller in THAT, I, 361) man's blessing God is an "expression of praising Thankfulness" (ein lobendes Danksagen), when the OT speaks of blessing God it does not "designate a process that aims at the increase of God's strength" (THAT, I, 361). It is an "exclamation of gratitude and admiration" (THAT, I, 357).
This is not at all a strange semantic phenomenon. If God is the primal and inexhaustible "blesser," then he must be above all others in a "blessed" state—the fullness and source of all "blessing." If this is so, then a most natural burst of praise would be "You are blessed!" That this recognition and joyful exclamation of God's blessedness should then be described as "blessing God" is not unusual. Other analogies, though not exact, would be our expressions like: "I magnify the Lord" or "Let us exalt his name." Both of these expressions properly recognize and give joyful expression to God's magnificence and his exalted status. They do not mean that we make God larger or higher. So to bless God means to recognize his great richness, strength, and gracious bounty and to express our gratitude and delight in seeing and experiencing it.
Here are some texts that have led me to these conclusions:
Deuteronomy 8:10 And you shall eat and be full, and you shall bless the Lord your God for the good land he has given you.
Here "bless" is virtually identical to "thank" or "gratefully recognize as the giver of blessing."
Psalm 100:4 Enter his gates with thanksgiving, and his courts with praise! Give thanks to him; bless his name!
Psalm 145:10 All your works shall give thanks to you, O Lord, and all your saints shall bless you!
Psalm 103:2 Bless the Lord, O my soul, and forget not all his benefits,
Psalm 96:2-3 Sing to the Lord, bless his name; tell of his salvation from day to day. Declare his glory among the nations, his marvelous works among all the peoples!
Here bless probably means: joyfully announce all these good things about God.
Psalm 104:1 Bless the Lord, O my soul! O Lord my God, you are very great! You are clothed with splendor and majesty,
This psalm begins and ends with "Bless the Lord, O my soul!" This probably means that the psalm is meant as the blessing. Therefore blessing God means heartily saying things like "God, you are very great!"
1 Chronicles 29:10 Therefore David blessed the Lord in the presence of all the assembly. And David said: "Blessed are you, O Lord, the God of Israel our father, forever and ever."
This is a clear example of what one does when one blesses the Lord: he calls him blessed! The same thing is seen in comparing Gen. 24:27 and 48.
Psalm 34:1 I will bless the Lord at all times; his praise shall continually be in my mouth.
Psalm 145:1-2,21 I will extol you, my God and King, and bless your name forever and ever. Every day I will bless you and praise your name forever and ever. My mouth will speak the praise of the Lord, and let all flesh bless his holy name forever and ever.
Psalm 113:1,2 Praise the Lord! Praise, O servants of the Lord, praise the name of the Lord! Blessed be the name of the Lord from this time forth and forevermore!