The one saving grace is that, generally, the collective public memory is short. In the immediate aftermath of the unfortunate incident the station's switchboard probably did load up with complaint calls, but in a couple of weeks most people who actually heard Chesner's outburst likely won't be able to remember who said what and on which channel it was said. (I say most people, although some never do forgive OR forget).
Many years ago, Joe Garigiola doing a live spot on the Today Show blew it and issued forth with a series of profanities that made Chesner's one-word expletive sound tame. Soon thereafter the incident became a broadcast memory, although many still recall what actually was said and who said it.
Given KETK's weather promotional campaign and the fact that Chesner is so new to the station, giving him the boot would be difficult, although some sort of punitive action by the station (short of dismissal) wouldn't be too far fetched. As was posted earlier, if the FCC comes calling the ramifications could get a bit more serious, for both the station and Chesner. Ideally, it will blow over, but there are those who possubly will not be willing to let the issue rest. KETK may at the outset do some sweeping under the carpet, but time may dictate that more be done. It's an unfortunate incident, but it has happened, still happens, and will continue to happen at stations everywhere.