"Come write me down, you powers above" - a fairly conventional poetic invocation of spiritual assistance in the task of recording the following fairly conventional tale.

"I've a diamond in my eye where all my joys and comforts lie" - sounds most uncomfortable, but a conventionally poetic way of saying he's looking at his (now) wife (see remainder of song).

For a really entertaining sketch of a later 19th century amateur poet, see Moggridge the customs officer in Arthur Quiller- Couch's Astonishing History of Troy Town. The rest of the book is worth a read too.