Green’s Dictionary of Slang

to persuade, to fondle.

c.1830		‘Smith’s Frolic’ in Holloway & Black II (1979) 61: I muched her over, and flash’d half a crown.
1953		Randolph & Wilson Down in the Holler 155: Much is a transitive verb meaning to praise, to flatter. One of our neighbors said to her husband: ‘Don’t keep a-muchin’ that young-un all the time, you’ll spoil him.’ The man was playing with his three-year-old son.