Sometimes the dictionary doesn't tell you the whole story. Every reference work I've seen puts the etymology of schmaltz as Yiddish shmalts meaning melted chicken fat, from Old German smelzan meaning melt. Indeed, the first recorded use of schmaltz in the figurative sense even mentions the etymology. It's from a 1935 article in Vanity Fair :
Schmaltz (cf. the German schmalz, meaning grease) is a derogatory term used to describe straight jazz.
So far, so not that interesting really. Schmaltzy = greasy. But today, only today I learnt that it's the smell and associations of the grease that are important. Melted chicken grease would be an integral part of the big family dinners that New York Jews associated with home, and mama and papa, and sentimentality and all of the other terrors of kinship. Thus schmaltzy = sentimental.
Schmaltz isn't just fat, it's family.
Home, sweet home.