One aspect of the weather that gets at least a little attention in gaming is the wind. The Moldvay D&D Expert rules had a 2d6 table for determining wind speed for sailing purposes. (This still didn't tie into any other rules, though, like penalties to missile fire for instance.) Most games I've run into that involved any amount of sailing have had at least a small table breaking out wind speed. Oddly, as much as I like pirates and nautical things, I don't have 7th Sea, 50 Fathoms, or Pirates of the Spanish Main RPG, so I can't say for sure about them.
But the nice thing about the Moldvay table, and its Rules Compendium descendant, is how easily it maps to the Beaufort Scale. The Beaufort Scale was developed in the early 1800s as a way to estimate wind speed from its effect on the environment, particularly in the formation of waves on the ocean. It ranges from 0 (calm wind, still water) to 12 (hurricane winds, waves 45 feet or higher). By working backwards, knowing the wind speed, a game master can use the Beaufort Scale to describe sea conditions. Using 2d6-2, a game master can dispense with the official table and just go straight to the Beaufort Scale, generating a result from Calm to Storm, leaving the Violent Storm and Hurricane levels of results as major events (as discussed in the Rules Cyclopedia, chapter 12, Strongholds and Dominions).
Rerolling wind speed every day on a 2d6 scale makes it pretty swingy. During one of Sir Francis Drake's voyages, his fleet was hit by gales for 52 days, making a very unlikely string of dice rolling, even if we consider all results of (9-2=) 7 and up as fitting the bill (Beaufort scale results of 7 are Moderate Gales, 8 are Fresh Gales, 9 are Strong Gales, and 10 are Storms). I'd recommend rolling once a week, and varying the daily wind speed by no more than one step up or down from there. Drake's string of stormy weather would still be pretty unlikely--at least seven straight 25% rolls--but a lot less unlikely than 52 of them.
Certain areas could have different dice rolls for wind speed. Trade winds tend to be pretty steady, and not too stormy, so maybe 2d3+1. A Sargasso Sea-type area, where ships are trapped by thick seaweed and light winds, could be d6-4. A continuous storm on a fantasy world, like the Eye of Abendego on Pathfinder RPG's Golarion would be something like d4+8.
One final note about the Beaufort Scale: wave height can be pretty important in a game. A ship is likely to capsize if it is hit by a wave more than twice its length if hit head-on or directly from behind (astern). If it's hit from the side (abeam) it will capsize if the wave is more than twice its width. Outriggers and catamaran style ships count the full width for this purpose...the Polynesians sailed the Pacific in these types of ships for a reason.