Macbook screen turns back on after suspend
Solution 1:
You are effected by this bug which appears to effect kernels 4.2 - 4.4 I suggest that you subscribe to the bug so that you can be notified of progress and the developers have a better idea of the impact it's having. As touched on by this answer by user 1783630 According to the author of the bug a functional workaround is to Disable XHC1 prior to sleeping by issuing the command
echo XHC1 > /proc/acpi/wakeup
However, the current content of /proc/acpi/wakeup in my 16.04 system is a bit more complex than that consisting of 4 columns of info covering Device, S-state, status, and sysfs node so I'm not convinced this is the way to go with Ubuntu. The bug has already been confirmed and triaged so hopefully this will be resolved with a newer kernel.
Edit: This related question also has some good answers that you may be able to modify to fit your circumstances
Source:
https://bugs.launchpad.net/ubuntu/+source/linux/+bug/1507472
Solution 2:
From the Arch Wiki entry for your model:
It may be necessary to disable USB's wakeup ability by by echoing 'XHC1' to '/proc/acpi/wakeup' in order to prevent immediate wakeup on suspend.
Once you tried it, you can put the line into your /etc/rc.local
file in order for it to be executed on every boot.