Since this isn't very formal, I'll just throw around ideas.
-Dominant hail sweeper. Currently probably the worst of the 4 weathers, how would this change things yada yada yada.
-This is probably a bit of a stretch, but what if we had two Pokemon, one of which "evolves" into the other, with basically similar movepools but with the unevolved one having less defense. We could thus analyze the pros and cons of evolution stones, and whether or not Chansey is better than Blissey, for example.
-A Pokemon not necessarily dangerous as a sweeper under a weather, but as a supporter, helping, in some way, other weather sweepers sweep much easier. Could this redefine our current idea of a weather team, especially "offensive" weathers such as sandstorm or rain? I could see this idea also working with a Pokemon that becomes a huge "stall" threat in a weather, being hard to kill and walling several things.
-Make an excellent sweeper with extremely poor typing in general, offensively and defensively. How badly does this affect his otherwise brilliant potential?
-Non-ghost type spin-blocker. I don't mean to eliminate types already, but spin-blocker and ghost are synonymous nowadays, and we could explore how needing a ghost affects the structure of stall teams, as opposed to a grass type or flying type or whatever.
-A DANGEROUS sweeper that really only works well with copious amounts of entry hazards (meaning 6 layers). How would this affect our current notions of semi-stall, stall or offense?
-a weather DISRUPTER. We know a Groudon summons sun, but CAP1 changes the weather to a random weather NOT currently on the field, meaning that you can't prepare for it at all. How could we see weather as a defensive rather than an offensive tactic, and how can a team employing this CAP make sure it isn't hindered by the random weather inevitably induced?
Lots of ideas here, none of which are very well formed. However I think some of these are pretty cool!