When you dip some bread into milk (or water, or wine, etc), the wet bread is called a "sop". So when something is "soppy" it is like bread made soggy with milk. We apply this to a persons' character to mean they are soft and overly-sentimental.
Soppiness is the state of being soppy.
Check the expressions "sopping wet" and "milksop" to get a further idea of this expression.