Something is definitely different between Office 2011 and 2016 for Mac. The man difference is the file sizes. When I copy pictures of graphs from Excel 2016 into Word 2016 the file sizes of the Word documents can be up to 20 times bigger than they used to be with Office 2011.
The work-around I've found is to save the Word document in .docx format, then save it again in .doc format (which is significantly smaller) and then to save again in .docx format which is then smaller than the intermediate .doc format document.
Here's an example. I pasted a picture of a graph from Excel 2011 to Word 2011 and then the very same picture from Excel 2016 to Word 2016.