I understand that there are a lot of things to consider when making this CAP but I think a lot of posts here have somehow transformed into supporting generically good typings and only barely relating it to the concept afterwards. Sure, checking X, Y, Z thing is helpful for Sun or Sand and we have to pick what is worth checking eventually and typing is the first and easiest step in doing so. That said... I personally am saddened by the lack of discussion on the weather itself and how CAP24 would benefit from the weather by virtue of its typing (as opposed to it just beating XYZ thing the weather struggles with). Having some aspect of its typing actually synergize with the weather is important to me so that CAP24 is encourages to actually utilize both of its weather.
As a brief interlude before I start talking about typings, I do just want to say that the ability to check XYZ has inevitably caused a certain Pokemon's name to come up quite a lot, and this mon's name came up quite a lot last CAP too. I'm talking about Tomohawk of course. Yes, Tomohawk is a staple in the metagame. Yes, Fairy and Flying-types generally do well against Tomohawk. However, in regards to a weather concept, I don't see why Tomohawk is all that relevant, let alone at the typing stage. Tomohawk is defeated by so many things other than just its opponent having SE STAB. Really, if we're worried about Tomohawk AND the concept simultaneously, then the biggest thing to talk about is Rain Dance Tomohawk and how Tomohawk on Rain Teams has the potential to mess with CAP24 if we don't handle typing properly. Well, that *would* be a big thing to talk about, except the part where there's probably even more threatening rain mons to consider... So uh, Tomohawk? I don't see it being as big of a thing for this concept as some people seem to think. Additionally, so many things handle Tomohawk without the merit of typing, including with just special bulk, toxic, neutral special attack STAB, SE special attack coverage, etc...
So, back to how CAP can directly synergize with Sun/Sand. Really, I think having at least one of our typings benefit directly from at least one of the weathers is important. People have already mentioned the Rock-type's ability to boost Sp.Def in the sand so I won't talk too much about that other than say I think it's pretty cool boost the merits consideration. Some people have also mentioned the Grass-type's ability to use Solarbeam, Solar Blade, and Weather Ball in the sun but have argued that Power Whip is just a better, more reliable version on Solar Blade. For the most part this logic holds true, but on the special side there's really no hard hitting equivalent of Power Whip that isn't legendary exclusive, which does leave Solarbeam with a potential niche. Solarbeam isn't uncommon on the Drought setter Zard Y, and if CAP itself can set Sun then I think Solarbeam is a usable move. Is it the end all be all? Definitely not. But I don't think it should be discarded from the get go. Some people have been knocking on the Grass typing as being offensively very poor. However, the metagame has seen an increase in bulky Water-types (to check Volkraken, etc, plus Arghonaut's sudden surge in viability after updates) and if we recognize Rain to be a problem to Sun/Sand then being able to hit something like Mega Swampert could be valuable as well. Is Grass on its own a great stand alone typing? No, it's really not that great on its own, but it does stuff at least. And luckily for us, CAP24 can have two tyings and not just one.
I think Grass/Rock actually synergizes pretty well, both with each other to remedy many of their weaknesses but also with the concept. Grass and Rock both gain a bit from the different weathers and neither are really hurt by the other weather (maybe being weak to Excadrill's Iron Head in the sand is scary, but it's not in the realm of impossibility to have stats compensate for this or to have teammates). I know the beginning of the thread had some support for this typing and then it died down, but really I think it's definitely got some merits. Its a typing that handles both of its intended weathers while getting feasible buffs while being able to handle opposing rain. The only things in the CAP metagame that resists both Rock and Grass STAB off the top of my head are Kitsunoh, Magearna, and Kartana, which really isn't that long of a list.
Deck Knight's suggestion of Rock/Dragon is something I think has potential and I could see it working, but being weak to a number of powerful Ground-types on Sand Teams is a bit scary to me (I think being weak to Excadrill's Iron Head is forgivable for Grass/Rock but remember that Earthquake has 20 more BP than Iron Head, so I am fairly concerned about our ability to handle that power increase). Dragon's defensive qualities are still a nice compliment to Rock's defensive weaknesses and helps CAP24 deal with Sun and Rain threats though, so it's not something I would dismiss outright.
Dragon/Fairy to me seems like a generically good typing and offers little benefit to the concept. Sure, it can beat up some opposing weather opponents but it stacks the Steel and Ice weaknesses that Grass/Rock has without any of the direct weather benefits that the later receives due to its typing.
In general I think reach has supported Water/Fairy quite well and he has linked it back to the concept better than others in the thread. However, Fairy/Water also suffers from the same generically good typing complaint as the above, just to maybe a bit lesser of an extent. I can see it working as a good anti-weather mon or even an anti-anti-weather mon beating anti-weather mons... but... to me the concept is weather, not anti-anti-weather and a bit of that synergy with the weather itself is lost in Water/Fairy in favor or just checking things that check weather. Really, one of my fears is that without direct synergy with the weather itself, the anti-anti-weather CAPmon just becomes... something good to use freely on non weather teams more often than on weather ones (anti-anti-weather doesn't inherently mean pro weather, especially without any direct benefits for the mon to use weather itself and I want a pro Sun/Sand mon morseo than just an anti-ant-weather mon).
In terms of DLC's suggestions, I personally like Electric/Flying far more than Fairy/Flying since I think DLC tried to sell Fairy/Flying as a great defensive typing but Electric/Flying just does it better in the current metagame. I'm not particularly fond of either because they lack direct weather benefits though, but I do like Electric/Flying far more than any of the Fairy types proposed so far... Really, I don't get the allue of Fairies for this concept, and you can see my above piece on Tomohawk and why I don't think it's that big of a deal.
So uh, those are my thoughts at this time. I personally want us to be pro Sun and Sand, not just anti-anti-weather. Sure both can happen, but I definitely want the the former alongside the latter and I don't want to see anti-anti-weather without also being pro due to its own synergy.
Also, more of an aside, Fire/Grass is something I haven't seen discussed but it also checks a number of my boxes in terms of having direct weather benefits, being neutral or positive vs opposing weather, and having a good mix of defensive/offensive qualities. Really the main problem with Fire/Grass is that it has SR weakness, which is why I prefer Grass/Rock, but I think this flaw is more forgivable than other flaws in this discussion.
/end another edition of HeaL's minority opinions.