How does meth use effect hypothyroidism medication?

It really doesn't: Except for the fact that levothyroxine should be taken on an empty stomach in the morning for consistent absorption, there is really no interaction between taking Methadone or methamphetamine (whichever you were talking about when you said "meth." here on the east coast, meth = methadone. As far as methamphetamine use goes, better not to use it at all, obviously!