Strangely high writes per second
Start with the open source sp_BlitzCache (disclaimer: I'm the maintainer of the project.) It's a script that analyzes your cached execution plans to find the most resource-intensive ones, and then tells you about design issues in those queries. You don't have to set anything up in advance - just install sp_BlitzCache and then run it:

sp_BlitzCache @SortOrder = 'writes'


Scroll across the result sets until you get to the "Writes" columns: 



That'll show you which queries are doing the most writes. You can scroll back across to the left to see the queries, their execution plans, and their anti-pattern warnings, and then work with your developers to improve them. (Or they might be totally normal: for example, based on your metrics, this might just be a case of someone logging data to tables.)