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1890, from mushy + -ness. Figurative sense of "sentimentality" attested from 1946.
"soft, pulpy, 1839; "sentimental," 1870; from mush (n.) + -y (2). Mush (n.) in a transferred sense of "sentimentality" is attested from 1908.
Sentimental: The kid got mushy with the broad/ If you expected Al Unser Sr to get all mushy-gushy and misty-eyed, you don't know Al Unser Sr (1839+)