Didn't the meek of the Psalms inherit the earth or the land, the Promised Land, that is? Nothing about a future paradise earth, but all about the now.
That's a good point....some of these psalms (e.g. 44:1-4, 78:54-55, 80, 105, 135:12, 136:21-22) look back to the mythos of the conquest (or the Abrahamic covenant in Genesis), and the description of the meek possessing the land has a timeless feel to it, like a proverb. In fact, there is a proverb almost identical to it: "For the land will be for honest men to live in, the innocent will have it for their home, while the wicked will be cut off from the land, and the faithless rooted out of it" (Proverbs 2:21-22). The general situation described in Psalm 37 is one of divine blessing that results from living faithfully, and thus does not pertain to any one particular time. Here are some parallels in the Psalms:
"All the ways of Yahweh are loving and faithful for those who keep the demands of the covenant...Who then is the man who fears Yahweh? He will instruct him in the ways chosen for him. He will spend his days in prosperity, and his descendents will inherit his land" (Psalm 25:10, 12-13).
"Blessed is he who has regard for the weak, Yahweh delivers him in times of trouble. Yahweh will protect him and his life; he will bless him in the land and not surrender him to the desire of foes...In my integrity you uphold me and set me in your presence forever" (Psalm 41:1-2).
"Your sons will take the place of your fathers, you will make them princes throughout the land. I will perpetuate your memory through all generations; therefore the nations will praise you forever" (Psalm 45:16-17).
"He drove out nations before them and allotted their lands as an inheritance; he settled the tribes of Israel in their homes" (Psalm 78:55).
"He confirmed it to Jacob as a decree, to Israel as an everlasting covenant: 'To you I will give the land of Canaan, as the portion you will all inherit' " (Psalm 105:10-11).
"The scepter of the wicked will not remain over the land allotted to the righteous, for then the righteous might use their hands to do evil" (Psalm 125:3).
There is also a favorite passage of mine from 1 Baruch: "O Israel, how great is the house of God! And how vast the territory that he possesses! It is great and has no bounds; it is high and immeasurable. The giants were born there, who were famous of old, great in stature, expert in war. God did not choose them, nor give them the way to knowledge; so they perished because they had no wisdom, they perished through their folly" (3:24-28).