I've often heard the theory that it was based on the Marauders seeing Snape cry at some point, but I remember when first hearing the nickname (long before I entered fandom), my immediate reaction was not that it was related to crying but related to complaining and whining, or even being sick . For me, Snivellus is pretty similar to Snuffles in that way: they both sound like four year-olds with stuffed up noses.