During the last round of the typing voting I did a rather large write up (that took me almost an hour and was completely removed despite it being crucial to my reasoning) on type frequency in the tier, both in general and usage wise. I'm not gonna redo the chart, but the most used by a significant margin are Water, Steel, and Flying (followed closely by Dragon and Fighting), with the least used being Normal, Ice, Dark, and Ghost. Due to its typing, I can't see this changing much at all.
Since I can't rely on it countering the types themselves, I must look at why these typed Pokemon are the most used. The answer is pretty obvious, of course, but lets have a look at the top 10 anyway. Let's look at the #1 most used Pokemon, Scizor. Scizor is a Bug/Steel type, great typing with its only weakness being 4x to Fire. Because of its Fire weakness, it benefits from rain, and it can survive perfectly fine in sandstorm due to its Steel typing. This makes it a great choice for those two weather conditions as well as ones fighting weather. Approximately 8 out of every 9 teams would benefit a Pokemon like this (Weatherless is ~49% of all teams, Sandstorm and Rain combined are ~39%, 88% is about 8/9). Politoed, obviously, is all but required to use Rain. Ferrothorn is much the same as Scizor in how and why it benefits from Rain and Sandstorm, and it resists Water, nullifying the power boost Water attacks get. Jirachi, same deal. Dragonite's typing lets it work excellently in both Rain and Sun (and, of course, teams trying to fight those) due to its resistance to both Fire and Water. Heatran is great in Sun because its Water weakness is nullified and it shuts down the other team's Fire boost, as well as Sandstorm due to not taking sand damage. Tyranitar is pretty obvious, same reason as Politoed. Breloom not only benefits from Rain because of its Fire weakness, but also gets STAB super effective against the Water and Steel types you're likely to find there (same with Sandstorm). Latios functions well in Rain and Sun for the same reason as Dragonite, but it also gets STAB super effective on those pesky Fighting types that give the Rock and Steel types that benefit from Sandstorm such a hard time.
After looking closer at this, I realized that actual typing isn't the reason why they're useful, although it is the reason why they're being used. My point being, the Pokemon and types that do the best usually do it because of weather.
"Robotnik", you might be asking, "are you saying this Pokemon should counter weather?" Kind of. If you look at my walkthrough of the top 10, you'll notice a lot of mentions to what types of weather it does well in, but also quite a bit about how well they do against the weather. So, I'm not saying it should counter weather directly. I'm saying that it should indirectly counter weather by countering the Pokemon that are good in it. To do this, we'll have to look at what Pokemon are good in weather and why. Let's look at the primary effects of each kind of weather (excluding hail because seriously who's doing that anymore):
Rain:
-reduces all Fire attacks' damage by 50%
-boosts all Water attack's damage by 50%
-activates certain abilities, alters the effects of certain moves
Analysis:
The Pokemon affected the most positively from being on this team are Pokemon that are weak to Fire, have an ability activated by it, and/or can use a move well that's positively altered by it. These Pokemon would usually be Water, Steel, Bug, Flying, Grass, and Electric. The Pokemon that would be best against it would resist Water and have super effective STAB on common Rain types, would also benefit from having an activated ability or a positively boosted move. These types are usually Grass, Fighting, Water, and Dragon.
Sun:
-reduces all Water attacks' damage by 50%
-boosts all Fire attack's damage by 50%
-activates certain abilities, alters the effects of certain moves
Analysis:
The Pokemon affected the most positively from being on this team are Pokemon that are weak to Water, have an ability activated by it, and/or can use a move well that's positively altered by it. These Pokemon are usually Fire, Grass, and Ground. The Pokemon that would be best against it would resist Fire and have super effective STAB on common Rain types, would also benefit from having an activated ability or a positively boosted move. These types are usually Water, Ground, and Dragon.
Sandstorm:
-damages any Pokemon that isn't a Ground, Rock, or Steel type or have certain abilities by 1/16th of their health per round
-boosts the Special Defense of Rock types by 50%
-activates certain abilities and changes the effects of certain moves.
Analysis:
The Pokemon affected most positively from this team would be Pokemon that aren't damaged by the effect and/or have an ability activated. These types are usually Ground, Steel, and Psychic. The Pokemon that would be best against it would have super-effective STAB, aren't damaged by the effect and/or have an ability activated. These Pokemon are usually Ground, Grass, Water, and Fighting.
"Holy Miltank, Robotnik! That's 11 types, that's the grand majority of them!" Correct you are, me. However, I'm not saying we should have to counter all these types. No, that would surely put us in Uber. Let's look at the types mentioned the most in this:
Water: 4
Grass: 4
Ground: 4
Steel: 2
Dragon: 2
Fighting: 2
Those were the ones mentioned more than once. Therefore, I think that this CAP should counter Water, Grass, and Ground (which it basically already does), while at least checking Steel and and Dragon.
As for what it should be countered/checked by, lets see what wasn't here:
Normal: 0
Dark: 0
Ghost: 0
Ice: 0
Rock: 0
Poison: 0
So, yeah, those. For those, I think it would be most realistic to try for it to be countered by Normal, Dark, and Poison.