According to Oxford, "muckle" is a dialect variant of "mickle", probably arising from confusion with "muchel" from "much"
And the original proverb (c.1599) was
"Many a little(/pickle) makes a mickle"
And referencing J O Halliwell's Dictionary of Archaic Words (which he produced back in 1847)
If that doesn't make you "mickled" (benumbed - Exmoor), and adding to the "muckle" (disorder - East.), consider that "muchelle" means dunghill
Simple Much?
For those who believe Val-Speak is indigenous to So-Cal
"much" (1) A term or expression of contempt common in old plays, and generally meaning little or none, far from it, by no means. It is similarly used as an adjective, in all cases inferring denial. (Halliwell, 1847)