"Weather radio", as in the NOAA weather bands, will not be affected by the digital TV transition. Only the radios that receive the TV bands (normally labeled as channels 2–13) will be affected, and the effect will only be to the reception of those (non-existent) analog TV bands.

As for getting a radio that can receive the digital TV bands, that may or may not be a future possibility. Since the audio and the video are multiplexed and encoded into a digital signal, the ATSC tuner electronics that are required to receive the audio would also have to receive the video. Standalone radios that receive the digital TV bands will probably not be manufactured, and the capability will be shifted to small portable TVs instead. That is only my opinion, though, and is based on the question, "If we have to put the same ATSC tuner chip in this radio as we would a TV, why should we pay all that money just to receive the audio?" That question is likely one to be asked by the manufacturers of these radios, and probably one that should be asked by the consumers as well.

There are issues with portable TVs, though. As said earlier, due to the way the ATSC signal is broadcast, it is very difficult to receive a usable ATSC signal while moving. That problem compounded by how difficult it is to simply receive an ATSC signal on a small portable antenna while standing still. A small portable antenna plus being on the move plus the ATSC signal probably equals a pretty black screen in most cases.