Editing fields presented in a view
One option is to use the field collection. and field collection views

This would automatically create the add edit and delete links to those who have permission to do so both in views as well as node view. It will popup a nice box to make the changes or add items. 

I followed the following steps.


Added a content type called Meter Reading
Added a field collection called Reading with widget embedded made its value as unlimited.
Add a field to the field collection.
Added a content of the type Meter Reading without entering anything in the reading. 


Now when you visit the newly created content you would get something like below image.



Here you will notice the add link this and when you click that you would get a popup something like in the below screenshot.



In the popup you can enter the readings. 

This is what I get after entering couple of readings. 



By the way you can add field collection with in field collection and it would work the same. So in your case instead creating a content type called Meter reading you can create a field collection called meter reading and then add a field collection with in that called readings and with in that add a field called Reading. 

So your entire page would look like this