Some cheap and dirty ideas:
barring teleportation, the PCs experience of weather is always localized. They are not likely to travel fast enough/far enough to actually see a meaningly difference in weather. As such, you only need to roll for the weather as "current relative to the PCs current position"
You could then roll up weather on a day by day basis (or get fancier) that you describe to the PCs. But not actually worry about modelling complex weather patterns.
Exceptions:
if the PCs do teleport (or other really fast travel to some place far enough to justify different weather) then there is even chances that the weather is the same, better or worse. You could easily just flip it. If it's raining where they started, it is NOT raining where the end up, That contrasts that they moved far enough away.
If the PCs arrive at a new destination, and the past local weather becomes important, just roll it up, like you did for the PCs.
Determining weather:
assuming your world has the same 4 seasons, either cheat and use last year's actual weather. Or make some fun tables. Make a table for each season. List out weather that ranges from nice and sunny to worst weather possible. Arrange the table in order for nicest to worse (so it progresses).
Then randomly pick a starting point on the table. Each day, the weather moves position on the table up or down by a 1d4-2 increment. Thus weather gets worse or better, but not supersonically radical.
You could actually roll multiple times per day (to better model weather changing over the course of a day).
You could pre-roll all this on your calendar for the year, so you basically know what the weather is all the time (less likely to forget, easier to incorporate into your descriptions).
That's Janx's free weather system.