Health app double counts steps I am using an iPhone 6 with iOS 9.3.2. It happens that Health app doubles step count (and therefore also doubles distance). I know this beacause the amount is too high (about double, I should be running to have >6 km/hour walking speed) and I beacause I tested it (I know the walking distance to my work because of Google) I have checked on Privacy which apps can write walking distance and I switched them off, however everything remains the same.

In addition, I checked Data sources on the Step dashboard on Health following fbara's suggestion. However there are only two apps on Data Sources: my Phone and Health App. None of the can be unchecked nor removed nor dragged up and down. The data  supplied by them is very weird: Health App supplies little steps certain specifics days while my Phone source supplies everyday almost all steps. Its supply is already doubled.

It is worth noting that for a long time I didn't have problems 

Thanks in advance!

Does some one know how to solve this?
It looks like the Health app is still (even after you turned things off) aggregating step data.  Instead of going to Privacy, go to the Health app.  Next go to the dashboard and tap on the Steps pane. Tap Share Data and then the Edit button on the top right.  Make sure only 1 app is supplying the step data, whichever app you want to use. 

While still in Edit mode, go to the Data Sources section.  Drag that single source to the top so it's the first row.  

Hopefully, this will prevent any other source from supplying step data.