No, there will not be unscripted weather. However, I agree. It would be great, but I think something that Spider-Man free-roam games have forsaken is the simple fact that fans don't play open world or free roam games to be a specific character; Fans play to be in the WORLD of that character. In other words, you're not playing as Peter Parker with spider powers, you're playing as you with spider powers. Obviously, because every choice you make, is your own, not Peter's or the game would be playing itself.
So one of the most important aspects of a free roam New York is immersion.
So that means rain, snow, cloudy weather, maybe just a windy day where trash blows along
Being able to destroy or interact with items in the city. To go inside of buildings if only to look around. Small things that allow players to simply enjoy exploration.
Interesting things that people say as you walk by. People with different clothing or interesting habits, like did you ever follow or stalk someone in GTA4 or like Shenmue?
4.) Random events.
It's cool to have variety in a city. Despite what individuals may say, statistically Spider-Man2: The Movie game was the most successful open world spider-man game. Maybe even the most successful spider-man game? It had: gang fights, gang members attacking civilians, thieves trying to break into buildings, gang hideouts, collectibles (exploration tokens and narrator hints that were funny and worth collecting), car accidents, people falling from heights, balloon kid, pizza missions, etc..The point is that there was so much to do that the game didn't feel strictly scripted. You had no idea what exactly would happen next.
5.) Day/Night cycles that the players doesn't have to control.
6.) Alt. Characters and Costumes. Just to change things up. However, since we have such great technology at our hands, we should be beyond simple skins. Each suit should have powers/codes attached to them.
Reboot Black suit: Infinite health
Classic Comic Black suit: Health regenerates 2x faster
Classic Comic Red/Blue suit: Move faster
Comic Scarlet Spider: Jump higher
Peter: No webs
....These are just examples, but you get the point.
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