Having thought about it bit more...
Weather avoidance is something that pilots normally request (rather then being offered). We then give clearances according to that request. This means that there is no real need to mention weather avoidance in phraseology (as the pilot knows already!).
Weather information on the ATC radar is useful (when displayed) to help anticipate requests for weather avoidance from pilots, but not as a sole means of determining the extent of and issuing 'avoiding' instructions.
Imperator1300