Until another user chimes in with specific possible causes, I will ask, does your phone ever disconnect from wifi when it is idle and unused for periods of time? This would cause the phone to fall back on Mobile Data and depending on what you are doing (streaming, updating, etc...) this can rack up data.
To add to that...pushed notification from various apps and email also use data. And as an iPhone user, I can tell you that my device disconnects from WiFi when it's been idle too long and only reconnects after I wake the screen. All of my notification that come during the night are certainly burning data, albeit not much, but data usage nonetheless...
I Have this problem too. It is using far more data than I have ever used and I haven't changed what I am doing. I don't stream things, but I have noticed that iTunes will turn on and start playing when I wake up phone.
Have you looked at Settings...Cellular to determine which apps are using the data?
Logging onto your Verizon account can tell you when the data was used.