Chrome taking up lots of space on my Android device
You might be browsing lots of and possibly media rich websites. To ensure this is the case, go to Settings &rarr; Applications &rarr;  list your system apps then select Chrome &rarr; Storage &rarr; Manage Space &rarr; delete the irrelevant data.

I once had 5-6 GB of space occupied by Chrome and I selectively cleared the irrelevant data. 




As for ADB backup issue, see this Github page.