A copy of the sheet music for this song can be found in the Levy collection at Johns Hopkins University. It's undated, but it looks like 18th century to me:

BUTTER & CHEESE,
A favorite
COMIC SONG,
as Sung with great Applause
BY
Master J. Meer,
At the different Theatres of the United States
Arranged for the
PIANO FORTE.
Philadelphia, George Willig, 171 Chestnut St

1
I've just come here before you.
Content you'll hear me sing.
I fear it is not in my pow'r
To do any such thing.
But since you're so inclin-ed,
I'll try what I can do,
And when I come to the chorus,
Why you may join in too,
Why you may join in too.

2
A cook I had for my sweetheart.
I'll tell you the reason why:
At christmas she baked plum puddings;
Likewise she made mince pies.
Her mistess's cupboard was of good store,
And she did keep the keys.
One pocket was filled with butter,
And the other she fill'd with cheese,
And the other she fill'd with cheese.

3
One pocket she filled with butter,
About a pound or more,
And in cutting of the cheese,
Brought the master to the door.
I being in a quandary what to do,
She bade me the chimney fly,
So up into the chimney
Went butter and cheese and I,
Went butter and cheese and I.

4
I hadn't been up the chimney
Above an hour at most,
When my butter began to melt,
And my cheese began to toast.
The master coming in the room,
He thought the devil was there,
For every drop that fell into the fire,
My eyes, how he did stare!
My eyes, how he did stare!

5
The master he went to the top of the house,
But not a word did he say,
Thinking that some water
Might drive this devil away;
And sure enough it came pouring down
As fast as it could fall,
And I came tumbling after,
Butter and cheese and all.
Butter and cheese and all.

6
And I came tumbling after,
With my sooty and greasy face.
Out of the front door I did run
And through the streets did pace.
The dogs did bark and the children did cry
As loud as they could bawl,
And the old women cried out of the window:
"There goes butter and cheese and all.
There goes butter and cheese and all."