My PC's are currently traipsing around in the jungle (on the Isle of Dread, or at least my version of it, specifically), and weather plays a limited but important role in the game. The most common weather effect is the one that is probably least mentioned - unusual cold and heat.
The way I've been mostly handling it is with some custom heat rules meant to be simple to use. Most heat rules usually call for hourly checks, which becomes hugely burdensome in long distance travel, and tend to produce unrealistic PC oriented results. (9-12 damage per day from ordinary summer heat, means that commoners should never survive an August.) So I've got my own daily heat effects table. Mostly the effects amount to your max hit points being a few points lower during daylight hours, and so the less hardy characters are relying on the cleric's Endure Elements spells. A few hit points gone, and a few spell slots used up is the extent of the weather for the most part.
Sooner or later its going to rain one night, and since the party lacks tents some characters probably won't get much sleep that night and will be fatigued and distracted the next day. Otherwise, rain is mostly a nuisance that means terrain is slippery when you run and charge and not a real danger - unless it is combined with extreme cold, in which case without proper gear it can be lethal.
Depending on the terrain the party might have problems with flash floods and the like if it rains hard. For 8th level characters, this is likely to a fairly trivial problem, unless for some reason no one in the party can make the survival roll for suitable camp site.
But really dramatic weather effects are pretty rare. Serious lightning storms are usually brief and don't happen every day. Serious wind storms are even rarer, and you might not see a natural wind storm over the course of a campaign. Serious hail is likewise rare. Seeing a tornado in person is for most people (without a car to chase them) a once in a life time sort of experience. Even in hurricane prone regions, a tropical storm is a once every 2-4 years experience and a full blown hurricane once a decade or so. Except for wetlands, major flooding is for most areas a once in a decade sort thing. Deep snows normally only happen every few weeks even in cold regions. In this sense, because weather of the sort that we think of as weather is rare, there is really not much reason to keep track of it or to use it as anything but a story element.
In such campaigns, weather need only occur in special weather generating places - Mount Awful, The Desert of Desolation, The Frozen Wastes, etc.
For me the principle reason to track weather is to remind myself it is there, and that it is a dial that I have access to in my story telling. At the very least, I like to have a background of normal weather so that when unusual weather happens, the PC's aren't immediately going, "Ok, so we'd better buff up, clearly something is about to attack us."
