To do something to the hilt means to give your all, to put forth the most effort possible. The idiom to the hilt seems to have come into use in the mid-1700s and calls upon the imagery of sword fighting. The hilt is the handle of a sword, dagger, knife, or other stabbing weapon.

What does back you to the hilt mean?

To the hilt and up to the hilt mean to the maximum extent possible or as fully as possible. [informal, emphasis] The men who wield the power are certainly backing him to the hilt.

What does defend to the hilt mean?

As much or to the greatest degree possible; completely or utterly. We're ready to defend our client to the hilt in court. ...