I'm experiencing the exact same problem. I received my new iPhone 7 two nights ago and connected it to my home WiFi network before bed. I had planned for all of my apps and iCloud photos to download while I slept. I woke up the next morning and my phone was connected to LTE. As I was no longer connected to WiFi, I used up my entire data allotment in one night! Thankfully, Verizon recognized that my data usage was abnormal for one day and restored it.
I have experimented with the Wifi connectivity issues and here is what I have discovered:
1. If my iPhone 7 is the only device connected to the WiFi network, I usually remain connected. However, the signal drops periodically.
2. If my iPhone 7 joins the WiFi network with my MacBook Pro and/or iPad Mini, the signal drops on all devices almost immediately.
3. If the signal drops on my MacBook Pro or iPad Mini, the only way to restore the signal is to turn off Wifi on the iPhone 7.
I was so distraught by the above turn of events that I ordered a new cable modem and Airport router. I will confirm whether this solves the problem. If not, I have an appointment with the Genius Bar on Monday and will probably swap out my device for a new one.