It gives a whole new perspective to the Lord's keeping the fat of beasts for himself. "...The priest shall burn them upon the altar: it is the food of the offering made by fire for a sweet savour: all the fat is the LORD's. It shall be a perpetual statute for your generations throughout all your dwellings, that ye eat neither fat nor blood (Lev. 3:16-17)."
There is fat for God, and there is fat for man. The Lord gives us fat as a sign of blessing and tells us to feast on fat ("And thou shalt eat before the LORD thy God, in the place which he shall choose to place his name there, the tithe of thy corn, of thy wine, and of thine oil, and the firstlings of thy herds and of thy flocks...").
Even the special priestly oil, which now belongs to all of us, is a sign of communion blessing.
Behold, how good and how pleasant it is for brethren to dwell together in unity!
It is like the precious ointment upon the head, that ran down upon the beard, even Aaron's beard: that went down to the skirts of his garments;
As the dew of Hermon, and as the dew that descended upon the mountains of Zion: for there the LORD commanded the blessing, even life for evermore.
Standing on God's hill, and having his fat olive blessing poured over us, is what dwelling in peace with brothers is like. Or dwelling in peace with brothers is what standing on God's hill and having his fat olive blessing poured on us is like.
God gives fat (God gives strength: lo que no te mata te engorda), God gives a home. So is our blessing commanded: life evermore.