I wouldn't say this is going to be a weatherless metagame, it's more that weather has been brought back down to a strategy on the same level as things like Trick Room and Gravity: Not a sure thing by any means, but potentially very rewarding.
Nobody has really been talking about Sun teams from what I can see, but there have been some significant changes to this playstyle.
Ninetales: Will-o-Wisp has received a very nice buff, which Ninetales has always been very good at using with her ample speed and bulk. As a status platform (and with proper rapid spin/defog support,) she can switch in multiple times over the course of the game, starting sun and crippling physical threats. However, not all is good for her; with the nerf to infinite weather, running Heat Rock can be very tempting, but Ninetales really misses Leftovers/Protect recovery. I'd love her to get Morning Sun as an egg move, but I'm not hopeful. With Politoed becoming less viable, Ninetales can also afford to run Solarbeam for added coverage.
Charizard-Y: With an astronomical Special Attack combined with a workable Special Defense, Charizard-Y functions as a much more offensive sun setter. With Sun up, Charizard can even afford to attack with fire both specially and physically, and will hit like a freight train either way, breaking through special sponges and defensive walls alike. Unfortunately, this uses the Mega slot, so I can't see Ninetales and Charizard-Y running on the same team as dual setters like Hippodown and T-Tar. Lack of variation in coverage, and poor defensive typings simply make that a really bad career move. However, on the subject of the mega slot...
MegaHoundoom: If MegaCharizard-Y hits like a freight train, Houndoom hits like a nuclear bomb. If you can switch in and wall a fire type, picking up a Flash Fire boost, and then Nasty Plot on the switch, you can incinerate half a team before sun runs out. Due to Solar Power reducing health, you're going to want to either get the job done quickly, or consider having Wish support. But on the upside, you have a lot of good synergy with pokemon such as...
Whimsicott/Jumpluff: These two grass puffballs have both received buffs to their usability as Sunny Day setters, with Whimsicott sporting an added Fairy type, and Jumpluff possessing slightly boosted special bulk. Both sport Memento and a way to use it before their opponent (Prankster/Chlorophyll), making them fantastic suicide sun setters (and great lures to fire type attacks for MegaHoundoom!) to get in, cause some trouble, set up Sun then bring in something else for seven turns of murder. In addition to this, they have great support options such as Sleep Powder, Encore, Leech Seed...All isn't good for them though, as a lot of their item options are going to be foregone in favor of Heat Rock.
Heliolisk: With the hidden ability of Solar Power, Heliolisk adds some much needed variety to the makeup of a Sun team, and can operate as a very nice Volt Switching scarf user, with fantastic coverage options.
Trevenant: With Harvest, Trevenant can be a very solid wall with Lum/Rest, or even Leech Seed/Sitrus. Unfortunately, due to the time limit on Sun, his ability may have just come a little bit too late to be of any importance.
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As far as I can see, the Weather game has indeed shifted towards 'do as much damage as you can with the short time you have available', which makes abusers such as Solar Power users and Chlorophyll sweepers much more relevant, at the expense of walling capabilities (Ninetales used to be able to take Scalds like an absolute champ, and heal it off with Leftovers/Protect: with the limited time of Sun, I don't see this happening as much anymore.) With proper support, however; say, a cleric like Sylveon or Florges, you can switch in Solar Power users repeatedly and burn holes in teams over a very short time.