Waiver is a noun with several meanings, including (1) intentional relinquishment of a right or privilege, (2) a dispensation, and (3) a deferment. In most cases, the one who relinquishes a right or privilege gives the waiver, while the one who benefits from the relinquishment receives the waiver. Waver is a verb meaning (1) to move unsteadily back and forth, (2) to vacillate, or (3) to tremble in sound.
Related distinctions apply to the verbs waive and wave.
Examples
Waiver
Oak Hills Local School District officials will apply for a two-year waiver to the all-day kindergarten mandate. [Cincinnati.com]
According to FCC rules, people who can’t get FOX can get a special waiver to receive a FOX feed from another affiliate. [KEPRtv.com]
Waver
In written responses to questions from the Washington Post and the Wall Street Journal, Hu showed no indication that China intended to waver from that path. [LA Times]
Much of our fresh resolve is already beginning to waver. [Financial Times]