You should search the DT and the forum for "Calton Weaver", which takes care of one bit of this. "The Weaver & his Shuttle" may well be an Irish song, but maybe only technically--I mean it might be a song produced in Ireland among Scots. Anyhow, the words would seem to be the same as those preserved in Peter Buchan's so far unpublished manuscript, "Secret Songs of Silence" at Harvard. Like this:
[This is from my in-progress "Musa Proterva"]
The WEAVER AND HIS SHUTTLE
1. Down by yon crystal river side,
Where Phoebus beams shine yellow, O;
I spied a pretty fair maid
That was baith brisk and mellow, O.
2. I stood a while and ponder'd,
To see her sweet behaviour, O;
She spoke wi' words most kindly,
Said — Ance I lov'd a weaver, O.
3. My heart did ake, I cou'dna speak,
To see a maid sae loving, O;
Then instantly, down by my thigh,
I found my shuttle moving, O.
4. My rubber strong, my need to please,
Put all things in good order, O;
This modest maid she asked me,
Gin I cou'd work her border, O.
5. On a bank o' broom I plac'd my loom,
Where primroses were springing, O;
My rural choice made birds to rise
And set them all a singing, O.
6. I hung my slaes to work at ease,
And kept a firm treadle, O;
I'm sure I drew twelve good long bores,
Before I broke a needle, O.
7. My treadle pin I fixed in,
Put all things in good order, O;
At every shot a double rock,
Until I wrought her border, O.
8. I pleas'd this jolly fairmaid,
Whose joys were wondrous double, O;
Though sorry at our parting,
She thank'd me for my trouble, O.
9. As she went alang, she sweetly sang,
The weaver and his shuttle, O;
Do far exceed in time of need
The doctor and his bottle, O.
10. So all ye pretty fairmaids,
And maids that sit a spinning, O;
There is a curious weaver,
Sae well can work your linen, O.
11. He works sae nice without a price,
The jolly handsome weaver, O;
And then for kissing fairmaids,
They count it as a favour, O.

__________________________________________________________ Peter Buchan, Secret Songs of Silence (1832), pp. 29-30. On the metaphor, cf. "The Bob o' Dumblane", "Let me in this ae night". The tune is a variant of Jockie's Gray Breeks; Burns says (note on this air, in Cromek [Reliques, 205] and Davidson Cook, 8): "Though this has certainly every evidence of being a Scottish air, yet there is a well-known tune and song in the North of Ireland, call'd 'The weaver and his shuttle, O,' which though sung much quicker, is, every note, the very tune." Buchan's song would seem to be the one mentioned; it will be noticed that there are some Hibernian touches to it. Burns directed his "My father was a farmer" to be sung to this air, whose Scottish version is the tune for Burns' "Again rejoicing Nature sees" (see in Dick, Songs, 68, # 67, and Kinsley, 313, #138), and appears in SMM I (1787), 28 (#27), to "Now smiling Spring again appears" (damned as "execrable" by the Bard), and Mayne's "Jenny's heart was frank and free", which is much better. The original words of "Johnny's gray breeks" are given by Herd (ed. Hecht, 1904), p. 184, and from the MS. by Dick, p. 375), a fragment of 8 lines beginning "I'll hae Johnny's gray breeks", and by Stenhouse (Illus., 27), 4 stanzas, beginning "When I was in my se'enteenth year", bearing no relation to Herd; though the prudent editor adds that he has "seen two additional stanzas to the song, but they appear to be the production of a different and very inferior pen; they are likewise coarse, and inadmissible on the score of delicacy." As Jocky's Gray Breeches the tune is in Oswald's Coll. of Curious Scots Tunes (1742), II.6, in 3/4 time, followed by a common-time version labelled "Brisk". Glen (ESM, 67) can't decide "whether there were two sets current at this time, or whether Oswald constructed the one tune from the other.". That's all I have at the moment.