HOWELL, thus is not related to the "thee, thou, thy" words. It means:
1. in the way just indicated; in this way: Stated thus, the problem seems trivial.
2. in such or the following manner; so: Thus it came to pass.
3. accordingly; consequently, therefore: It is late, and thus you must go.
4. to this extent or degree: thus far."
I hope this helps. It is usually used in place of "therefore," IMHO. For instance, "She could not swim, thus she did not want to go to the beach."