iTunes keeps syncing my unchecked songs to my iPhone
Have you got Autofill activated?

Autofill can be used with either automatic sync or managing your content manually. When using automatic sync, simply select/deselect the Automatically fill free space with songs option found on the Music sync settings.

This option automatically selects music to fill the remaining space on your device. It does this by filling up the space that isn’t already being used up by the music, videos, books, apps, podcasts, etc you’ve manually selected. 

This random selection will also adjust automatically as you make changes in the future. For example, iTunes will automatically remove some of the “autofilled” songs to make room for other things you manually select as wanting to sync in the future.

NOTES:


Each time you select/deselect the Automatically fill free space with songs option found on the Music sync settings option, you need to perform another sync for it to take effect on your iPhone.
If you've been managing music manually, the Autofill option is found in the On This iPhone section of your iTunes device sync settings. It appears as a button that does the same thing I described above but also provides an additional drop-down menu to the left that allows you to limit the Autofilled music to a specific playlist rather than randomly selecting content from your entire music library.