Sorry, folks, but this is a word of VERY tenuous provenance. I tend to disbelieve the "shuttle" theory. It sounds more to me as though people down the years have jumped on the continual knocking of the shuttle was at least a surety that you'd be able to eat explanation; of Reinhard's post & Nigel's link; as "it sounds right, so it must be right". The more likely explanation would be that since guttle only seems ever to appear in that song as a RHYME...

Except that... ;-)

Consulted a dictionary or three. According to Partridge's Dictionary of Slang, guttie has more than one definition. The obvious one, well known to history or anyone with a knowledge of golf, is that golf balls were originally made from gutta-percha & therefore referred to as 'gutties', probably long after they stopped being made from gutta-percha. But Partridge also give a definition of 'glutton', presumably a glutton being someone that is "gutty".

"But the word is guttle!", I hear you cry. The following entry in Partridge is guttle-shop. AHA! A 'guttle-shop' is a tuck shop. For those of you, probably non-UK (or Oz) not familiar with 'tuck', it refers to food. A tuck shop, loosely, was/is a shop in a public (i.e. fee-paying) school where you can buy provender additional & supplemental to the school menu. These days, most folk think of tuck (if they think of it at all) as being sweets & snacks, but the food at a public school could often be pretty basic (reference Kipling's oblique comments about the diet at Westward Ho!), so it wasn't necessarily just "sweets" in regards to food, and might include non-food items too (many do today).

The fly in the humbugs, potted meat, whatever, is that Partridge gives 'guttle shop', very specifically as being slang of the 19thC from Rugby School (AHA!). The obvious question now is, how old is Poverty Knock (Chumba's notes as given above being no indication of anything)?

The cautious conclusion (and it is always wise to be cautious where etymology is concerned) is that we definitely have provenance that 'guttle' is a genuine word, not something invented to rhyme; either dialect or slang; that refers to food & to eating. However, it would seem difficult and/or unlikely to form a connection between Public School slang & dialect referring specifically to weavers. Why would it have passed from one to the other, either way?

It looks like it's a real word referring to food / eating; any direct connection to weaving very much appears to rely on the fact that it rhymes with shuttle. If you see what I mean... ;-)