The weather system in SH3 is an PITA.
You may have more luck with SH3Weather, it should be available in the MODS section.
Just so you know. IIRC the weather in SH3 has a randomly calculated chance of changing every 48hrs (game time) but if you save & reload that internal timer is reset and you start again.
From experience, the weather seems to change more often when you spend lengthy amounts of time submerged. This is just my observation and I'm sure there is no hard data to back it up. However, I find that if I'm stuck in prolonged heavy rain, fog, seas then diving usually helps.