Tried another shot at it and I heard the following. Let me know if you folks agree. There's still one line about the preacher and rooster that's unclear. I proposed "{Who through the 'hind}, and didn't have a stew?", but I'm not sure. All else, I think works...

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Tight Like That - lyrics (Huddie Ledbetter)

Guitar intro [3 measures]

Oh, it's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Guitar break [2 measures]

Oh, it's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

You take Sal and I'll take Jane
They both good lookin', but they ain't the same
It's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

If you want to see a preacher laugh
Change a dollar and a-give him a half
He's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Some folks said that a preacher won't steal
I caught two in my cornfield
It's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

One had a match and one had a sack
Gone out to cornfield just like rats
It's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Some folks said that a preacher won't steal
I caught two in my chicken-roost
It's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Who through the 'hind, and didn't have a stew?
Tryin' to catch a rooster, make rooster soup
It's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Preacher and rooster had a terrible fight
Preacher knocked the rooster clean out of sight
He's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Preacher told the rooster, "That it'd be all right.
Meet you at the hen house t'morrow night
It's tight like that. Ooooh! It'd be tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Yeah!
Guitar break [2 measures]

Oh, it's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Cold frog jumped in the bottom of da' well
Oh, by God, he jumped into hell
He's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Funniest thing that I ever seen
Tomcat sitting on a sewing machine
He's tight like that. Ooooh! He's tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that

Guitar break [2 measures]

Oh, it's tight like that. Ooooh! Tight like that. Ooooh!
Hear me talkin' to you. Oh, it's tight like that.