Weather in a Rockstar game exists between ambience and systems. Here we look at what's likely for GTA 6.
Storm footage has its own breakdown in the storm scenes piece.
What's likely
Rain will happen. Sun will happen. Cloud cover will happen. Wind effects - likely visible. Lightning - likely with storms. Day-to-day changes in weather - will happen.
Florida-specific: afternoon thunderstorms. Hurricane-force events as occasional set pieces. Heat shimmer on the highways. All plausible considering Florida weather in real life.
What's possible but not certain
Dynamic flooding (rain collecting and changing how you get around). Dynamic tide (sea levels going up and down). Hurricanes as repeating dynamic content. Animals that react to the weather.
RDR2 showed examples of these. It's unconfirmed whether GTA 6 will carry them over.