How can I keep my Apple Watch from draining my iPhone's battery?
What does usage on the iPhone say? 
Have you contacted Apple Support to check the power diagnostics at https://www.apple.com/support/iphone/repair/


Once you have some measurements and data, you can change which apps get notifications, which apps are allowed to run in the background and which apps do background refresh.

You can use the Apple Watch app to deinstall any apps you need to test their power usage and also look at the power usage on the Apple Watch.

People that have honed their iOS power needs over the last 6+ years now have to consider a totally other use case. Now iOS can act as the server backing the Apple Watch as it offloads all of the third party app workload to the iPhone.

Basically, you measure the usage on both devices. Try some changes to minimize the highest users, and then repeat to balance functionality and energy use.

Before watch, my iPhone 6 would end the day with 50 to 30% charge always and when it didn't I knew exactly why I was burning power at a faster rate and planned a charge to compensate. 

It's taken a week to sort through Apple Watch and iPhone and I'm actually at better energy use now since I've stopped using the iPhone for some things and have rejected most Apple Watch apps as slow remotes for the iPhone. My glances are down to 6 items I need and 2 for fun. My Apple watch also is making it all day with plenty of power to spare unless I exercise with it for 3 hours a day. That's the only time I've had to do a mid day charge on the watch.