Cinccino -- Weezing takes 41-50% by Life Orb Tail Slap, Cinccino's main STAB attack. It's a solid check, but not a counter because Weezing loses if it's weakened a bit. Choice Band Cinccino does 49-58% to Weezing.
Amoonguss -- Weezing does beat Amoonguss if it's already used Spore, but so do many other Pokemon. Many other Pokemon also have much more offensive prowess than Weezing.
Gardevoir -- Gardevoir can switch in and OHKO Weezing.
Absol -- Weezing beats this, but if Absol gets a Swords Dance up, Weezing has trouble against Absol. There are two luck instances where Weezing can be beaten by Absol: 1) Will-o-Wisp missing 2) Night Slash's 25% chance of critting
Golurk -- Weezing counters Golurk.
Alomomola -- Weezing does do well against Alomomola, but it can always get burned by Scald.
Emboar -- Emboar can switch in and KO Weezing. Also can use Weezing as Substitute bait.
Armaldo -- Not particularly difficult to beat, but Weezing counters this.
Sawk -- Weezing counters this.
Miltank -- Weezing can beat Miltank 1 vs 1.
Exeggutor -- Exeggutor easily OHKO's Weezing with Psychic and isn't OHKO'd by Sludge Bomb.
Braviary -- Weezing can't even check Choice Band or Life Orb Braviary because it's easily 2HKO'd by Brave Bird. SubBU Braviary uses Weezing as set up bait.
Eelektross -- Weezing beats physical variants but gets destroyed by special.
Skuntank -- Weezing loses to Skuntank 1 on 1 because Skuntank can Taunt it.
Ludicolo -- Ludicolo isn't OHKO'd by Sludge Bomb and Ludicolo 2HKO's with Hydro Pump.
Altaria -- Weezing loses to the most common variant, Choice Specs. It beats Dragon Dance variants though.
Golem -- Weezing beats this, not particularly hard to defeat though.
Musharna -- Musharna uses Weezing as set up bait.
Samurott -- Special Samurott easily defeats Weezing. Physical Samurott loses unless it has Lum Berry.
Haunter -- Haunter uses Weezing as set up bait.