The DT file THE KEEPER is described as "This version by the Weavers"; no traditional source is named. It is a "condensed" arrangement, with a new final verse added, of the set published by Cecil Sharp which I refer to below.

The eight(?) texts Kevin has found (including the Weavers' set again) all derive from a single source; the version of the song noted by Cecil Sharp from Robert Kinchin at Ilmington, Warwickshire, on the 23rd. August, 1909. Sharp published it in Novello's School Songs (1909); English Folk Songs, Selected Edition vol.II (1921) and One Hundred English Folk Songs (1916): this is the song that so many of us remember from Primary School. Sharp edited the text, partly because Kinchin's was a little muddled, and partly because the sexual sub-text of the original was still obvious enough to make it, in those days, unsuitable for children, and undesirable to publishers. Kinchin's text can be found in a number of more recent publications.

The Hunter (above) is a modern re-write by one Jack Splittard: © 1959 Atzal Music, Inc., New York. It was recorded by The Kingston Trio.

The verses above beginning The seventh doe did run to the east and The eighth doe served upon a plate are modern additions of the "Ren Fair" type, made by people who have taken the song literally. The verse ending She looked so sad that he let her go is modern, too.

Oddly enough, the second of the MP3 verses at the Cantaria site is actually (loosely) based on a genuine (broadside) verse (see the final link in this post).

With due respect to Kevin, many websites will put any old stuff up, usually without any attempt at crediting any source or providing reliable information; and with no distinction made between traditional versions of a song and modern recordings. This is certainly the case with some of the material above. It might be best to re-post the Sharp set here, first as originally published:

THE KEEPER

(Noted by Cecil Sharp from Robert Kinchin at Ilmington, Warwickshire, 1909. Edited text.)

The keeper did a shooting go;
And under his coat he carried a bow,
All for to shoot at a merry little doe.
Among the leaves so green, O.

Chorus:

[1] Jackie boy! [2] Master!
[1] Sing ye well! [2] Very well!
[1] Hey down, [2] Ho down,
[1] Derry derry down,
[1&2] Among the leaves so green, O!
[1] To my hey down down, [2] To my ho down down,
[1] Hey down, [2] Ho down, [1] derry derry down,
[1&2] Among the leaves so green, O.

The first doe he shot at he miss'd,
The second doe he trimm'd he kiss'd,
The third doe went where nobody wist.
Among the leaves so green, O.

The fourth doe she did cross the plain,
The keeper fetch'd her back again.
Where she is now she may remain,
Among the leaves so green, O.

The fifth doe she did cross the brook;
The keeper fetch'd her back with his crook;
Where she is now you must go and look
Among the leaves so green, O.

The sixth doe she ran over the plain;
But he with his hounds did turn her again;
And it's there he did hunt in a merry, merry vein
Among the leaves so green, O.

From One Hundred English Folk Songs, Cecil Sharp, 1916.

Now, as originally noted from tradition:

THE KEEPER

(Noted by Cecil Sharp from Robert Kinchin at Ilmington, Warwickshire, 1909. Original text.)

O the keeper he a-shooting goes
And all amongst his bucks and does,
And O for to shoot at the barren doe
She's amongst the leaves of the green O.

Chorus:

Jackie boy, Master,
Sing 'ee well? Very well.
Hey down, Ho down,
Derry derry down.
She's amongst the leaves of the green O.
To my hey down down, To my ho down down,
Hey down, Ho down, derry derry down,
She's amongst the leaves of the green O.

The first doe that he shot at he missed,
And the second doe he trimmed he kissed,
And the third ran away in a young man's breast, *
She's amongst the leaves of the green O.

The fourth doe then she crossed the plain,
The keeper fetched her back again.
O and he tickled her in a merry vein,
She's amongst the leaves of the green O.

The fifth doe she crossed the brook,
The keeper fetched her back with his long hook,
And what he done at her you must go and look,
For she's amongst the leaves of the green O.

The sixth doe she ran over the plain;
But he with his hounds did turn her again;
And it's there he did hunt in a merry, merry vein
Among the leaves so green, O.

Roud Folk Song Index number 1519.

From Cecil Sharp's Collection of English Folk Songs, vol.II, ed. Maud Karpeles, 1974.

* It should be noted that James Reeves (The Idiom of the People, 1958) quotes this line from Sharp's MS as And the third ran away in a young man's heart.

Other collectors found similar versions of the song, but due to its content (mild enough to us, but considered gross by many in those days) these were not published at the time; except for a set which appeared in Sabine Baring Gould's Songs of the West. This text was re-written to make it "safe", but makes it clear, as the Sharp re-write does not, that the "does" are actually women. Commenting on another set, this time noted by Ralph Vaughan Williams in Cambridgeshire, Roy Palmer (Bushes and Briars, 1999) notes:

"The earliest known version is a black-letter ballad of fifteen verses, written by one Joseph Martin, and published in the mid-1680s under the title of The Huntsman's Delight; or the Forester's Pleasure. In the eighteenth century a slightly less elaborate version was issued, this time in white-letter, with only six verses, and entitled The Frolicksome Keeper. A New Song. Unlike its predecessor, it has the dialogue chorus which is common to versions which have turned up in oral tradition during this century."

A copy of the second broadside alluded to can be seen at Bodleian Library Broadside Ballads:

The frolicksome keeper. A new song.  Harding B 22(100): printer and date unknown. The real meaning of the song is rather more apparent in the broadside text than in those we have here.