My bigger concern is that each side can have different weather, this makes no sense to me. If your turns are simultaneous it would correct that.
I just posted a similar response in a Steam forum, so I thought I'd post it here as well.
This is something that comes up from time to time, and my arguments are that simultaneous turns/weather don't quite work out as one would hope for with a game that has one side start, and the other side go second under the same date.
For example, Axis goes first in most of the campaigns, so the Allies are always second under any specific date, i.e. before the date and weather advances to the next turn date and weather.
Essentially from 1939 to let's say 1941, when the Axis are on the offensive, the Allies can always be guaranteed to defend/respond to any Axis aggression with the same weather.
However, once the balance tips and the Allies go on more offensives later on in game, because the Allies go second under a specific date, the Axis, which is now on the defensive, is not guaranteed the same weather to respond to any Allied attacks.
Why? Because the date rolls over to the next date after an Allied turn, and the weather only possibly changes between Allied and Axis turns, whereas the weather is always guaranteed between an Axis and Allied turn when you play with same weather for both sides.
Playing with the same weather for both sides of a turn, is only the same weather for the Axis and then the Allies, but not necessarily the same for the Allies and then Axis.
Over time I would argue that this system actually gives an advantage to the side that goes second in game. This is because the side that goes second is guaranteed to have the same weather as the side that goes first (all game), while later on in game it will have an opportunity to have good weather (from time to time) on its offensive turn where the defending side is not necessarily going to have good weather when it comes time to initially respond on its follow up turn.
Hopefully that makes sense,