From Middle English mukel, muchel, from the same source as (perhaps a variant of) mickle, which see.
The NLS text has the word ane after muckle which clearly scans better for reading.
Gin ye can licht on ony dacent sensible wumman o ' your ain age I 'm nae jist carin ' sae muckle.
Besides Mainland, the principal member of the group, the more important are Yell, Unst and Fetlar in the north, Whalsay and Bressay in the east, Trondra, East and West Burra, Papa Stour, Muckle Roe and Foula in the west, and Fair Isle in the south.
The gate they're gaun the noo, they couldnae win through an the muckle deil were there to pilot them.