This old dialect saying is often taken to mean that a lot of small (mickle) things together add up to a lot (muckle.) In that case it would be saying rather like "Look after the pennies and the pounds will look after themselves" – in other words, it's most important to concentrate on small things, and these will grow into big things by themselves.
However, "mickle" and "muckle" originally meant the same thing – a lot, plenty. This can be seen in older texts like John Keats's early 19th century poem "The Eve of St Agnes" where a character says "Let me laugh awhile; I've mickle time to grieve." In that case the meaning would seem to be "if you put a lot together, you get a lot more" which is undeniable but not very illuminating. The likeliest explanation is that the word "mickle" changed its meaning over time to "little."
However, "mickle" and "muckle" originally meant the same thing – a lot, plenty. This can be seen in older texts like John Keats's early 19th century poem "The Eve of St Agnes" where a character says "Let me laugh awhile; I've mickle time to grieve." In that case the meaning would seem to be "if you put a lot together, you get a lot more" which is undeniable but not very illuminating. The likeliest explanation is that the word "mickle" changed its meaning over time to "little."