Smart man once said, "Pokemon with double weaknesses won't be good defenders anymore." Okay, it was me, I sad that. But Exeguttor might be able to. Let's see why.
Exeguttor was fairly common in gyms, in part due to his relativly high max CP of 2900+ and in part due to his awesome stats.
First thing you notice is his high ATK stat (of 233) which is very close to the best attackers. Some common Pokemon with similar stats are Gyarados, Machamp, Jolteon and Arcanine.
Next up, really good stamina (of 190) what is also close to the top along with Slowbro / Slowking, Gyarados, Umbreon and Clefable.
DEF stat (of 161) is not that great tbh, but it's not the worse also. Machamp and Arcanine are Pokemon with siminar DEF stat.
Stats seem okayish, let's look deeper.
Exeggutor is Grass and Psychic type Pokemon.
That means he has a double weakness to Bug type attacks.
And is also weak to a lot of Pokemon type attacks like: Fire, Dark, Flying, Poison, Ghost, Ice...
Before I get any deeper lets talk about Exeggutors attacks.
Saidly, it's best Quick attack is Confusion. I said sadly because it's a legacy moveset now. None of the new moves are really close to it, so a little bit of disappointment to anyone who doesn't have one.
Why is it so good? It's the only attack that deals 20 damage (also Volt Switch). And that hurts in real life situations. It hurts a lot. You just have to dodge every attack if you want your Pokemon to survive until the end of the battle.
What about charge move? No legacy movesets here so you can have the best one. But which one is the best? It's really hard to decide. Solar Beam is a one bar charge move that deals 180 damage, and Psychic is a one bar charge move that deals 100 damage. So we have a clear winner? Maybe, maybe not. I think I would still prefer Psychic.
Solar Beam is weak against Bug, Dragon, Fire, Flying, etc. So pretty much everything you will get attacked by. And it's also easier to dodge than Psychic.
Big question! Can it overcome double weakness? Lets see.
Best Bug type Pokemons with Bug type attacks are Heracross, Scizor, Pinsir and Forretress (no, I don't count Parasect, we're not trying to prestige over here).
Heracross is also a fighting type, so it take more damage from Psychic type attacks. So he is of the list. (also, many people aren't even able to have him).
Scizor and Forretress are also Steel type Pokemon, that means they take less damage against Psychic type attacks. But only Scizor can have two Bug type attacks.
And there is also Pinsir, pure Bug type Pokemon that can also have two bug type attacks.
If you didn't know, you can use X Scissor (Scizor and Pinsir have that Charge attack) between two dodges of Counfusion.
You know what they all (Scizor, Pinsir and Forretress) have in common? They have really low stamina and HP. And also are not really easy to find. And how many people have powered up any of them?
Combine low HP with Confusion that deals 20 damage, means you have to dodge perfectly. And if you can do that, you can pretty much win with everything.
So best counter would be Scizor, Pinsir, Flareon and Gengar. But they all have low HP.
So, i think it overcomes double weakness. Is it perfect? No, but no one is. I would put him in Tier II and definitely Top 6 Gym defenders right now.
Sad thing is, the best Quick attack move is a Legacy one. (good thing I have 100% IV Exeggutor with Phychic )
And don't ignore the fact that Exeguttor is the best Pokemon that can have Solar Beam (link). So if you need counter for Vaporeon, look no further. Bullet Sead and Solar Beam on Exeguttor will tear down anyone.
Good luck using your Exeguttor.