Tweak-SSD reports that AHCI is disabled. Why is that?

To learn what AHCI is, please have a look at Wikipedia:

http://en.wikipedia.org/wiki/Ahci

Tweak-SSD does check if AHCI is enabled in Windows. If not, TRIM is not supported on your system. However, you may want to try to enabled it manually by opening regedit, and navigate to this key:

On Windows 7:

HKEY_LOCAL_MACHINE//SYSTEM//CurrentControlSet//Services//msahci

On Windows 8:

HKEY_LOCAL_MACHINE//SYSTEM//CurrentControlSet//Services//storahci

The value called 'Start' must be set to 0

Also ensure that AHCI is enabled in your system's BIOS.

If the whole key is not there on your system, then there's nothing you can do about that.