These are my "records" as Gavin Greig would say, as I have them in my long-in-transit project of an anthology of Scots bawdy songs.

THE DUNDEE WEAVER

(A)

1. O I'm a Dundee weaver, and I come fae bonnie Dundee,
One day a Glasgow fella came a-courtin me,
He took me oot a walkin doon by the Broomielaw,
And there the dirty wee rascal stole my thingamajig awa; Aye there the dirty wee rascal stole my thingamajig awa.

2. He took me oot a picnic doon by the Rouken Glen,
He showed to me the bonnie wee birds and he showed to me the hen;
He showed me every birdie frae a lintie tae a craw,
Aye and he showed to me the bird that stole my thingamajig awa. [bis]

3. Noo I'll gang back to Dundee lookin bonny, young and fair,
I'll put on my ribbons an' reels an' tie up my bonnie broon hair,
I'll put on my corsets tight to mak my body look sma',
And wha will think wi ma rosy cheeks, that my thingamajig's awa. [bis]

4. Now come all ye Dundee lassies, tak this advice fae me,
Never let a Glasgow lad an inch above yer knee,
Never stand in the long grass or up against a wa',
For if ye dae ye can safely say that your thingamajig's awa. [bis]
_____

From the singing of Hamish Imlach, Glasgow, c. 1963/4.
A variant version [learned from Robin Hall] sung by Arthur Argo on his record "A Wee Thread o' Blue" (Lyrica Erotica vol. 2), Prestige/International 13048. Differs as follows:

1.2 I met a Glesgy fella an he came coortin' me; 1.3 Kelvin Ha', 2.2 a bonnie wee hen, 2.3 the bonnie wee birds fae the lintie tae the craw, 2.4 Aye, he 3.1 But I'll gae 3.2 Oh I'll pit on my bucklin' shoes 3.3 An' I'll 3.4 An' fa will ken 4.1 Sae a' ye Dundee weavers, 4.2 Oh never let a fella 4.3 Oh never lie 4.3 'Cos [etc.]. Another variant of 4.3 I have heard is "Never stand at the back o' a close".

St. 4 has the cliché of the "inch above the knee", found in many songs of this type on both sides of the border (cf. "Robin was a Ploughboy", e.g.). 'Bird' in 2.4 of course = "penis", a common metaphor, probably from its mysterious ability to rise. Another variant line heard 1959 (Glasgow), has "cock" as a partner for "hen".
The tune appears to be a set of The Lincolnshire Poacher ("It's my delight on a shiny night in the season of the year"), also used for the teasing "Knock knock knock" song, expurgated slightly for Tin Pan Alley as "The Thing". The English tune was also plagiarised by Sir Harry Lauder for "It's Nice to Get Up in the Mornin'."

(B)

1. O I'm a Dundee weaver, I come frae bonnie Dundee
I fell in love wi a sodger lad, and he in love wi me;
He took me for a walk ae nicht aroon the back o' the Law,
An' what dae ye think o' ma sodger lad, for ma thingamajig's awa'.

2. Come all ye Dundee weavers, and tak advice frae me.
Never let a soldier lad an inch upon [!] yer knee,
Never let him back ye up against the wa',
For if ye dae ye may safely say ye're thingamajig's awa.

3. O I'll awa' hame tae Dundee while I'm sae young an' fair,
I'll pit on ma silken goon and comb ma golden hair,
I'll wind ma corset roond me tight tae mak my body look sma',
For wha's tae ken by ma rosy cheeks ma thingamajig's awa'.
__________

From R.H [maybe I'd better not identify him further], Salt Spring Island, B.C., April 1990; learned from two Dundee lads in 1942, in a prison camp (24D) at Posen (Poznañ), Poland. "The Law" has to be a local mountain, but its whereabouts are another thing. We have a "West Law" at Leslie in the middle of Fife, but it's too generic a name to specify.