After a recent update either to the app, or iOS 9.3.5, this app started chewing up my battery, draining my iPhone 6 in about 2 hours.
Turning off background activity settings didnt fix the issue, and it kept accessing HealthKit in the background draining the battery.
Uninstalling the app immediately pulled my CPU load down from 100% to a low idle.
Shame, it was a pretty useful app, but not worth bricking my battery for.
shdwshard about MyFitnessPal: Calorie Counter, v7.1.1