Well, "it sounds nice" might be one answer but, grammatically it doesn't make much sense.
Weather forecasts are notorious for hacking up the language. Don't look for good grammar there.
edit: Although I have not heard may described as a "helping verb" this certainly does not mean that it isn't one. I've always considered may as a modal verb (according to the Oxford Dictionary). But, the original question here was the use of "may possibly" in the same sentence and, as Susieqd says, the idea is OK.
Student or Learner