My only source is having read Russian novels in English. I wonder if the "little" water is like someone's diminutive name, i.e., meant to show familiarity or affection. Like, Mishka is the diminutive of Mikhail.
English has several form of diminutive that are still in use but only -ie seems to be still somewhat productirlve (i.e. used to produce diminutives of new words).
-ie (doggie)
-let (booklet)
-ling (duckling)
-ette (cigarette)
None of which seem to work well with "water" (waterie, watelet, waterling, waterette)
* вода - voda - water
* водка - vodka - vodka