Ok, so Charizard has two major weaks
Characters that can easily get him in the air (and keep him there)
Characters that can pressure him from far away
Zard's air speed is one of the worst in the game, ESPECIALLY for a large heavyweight. And his aerials are absolutely god awful at protecting him when he's in the air. Fair covers maybe 1/4 of his body (compare to Sheik or Bowser fairs with their large radius) and is very slow to end (compare to ROB or Sheik fair). Bair is slow as **** to start and end. Uair only protects his head. Dair is even slower than bair. Nair is the best because it covers everything, but does not actually have much disjointed range to beat out other aerials. This is important. HOWEVER, the autocancel window is very close to when the hitboxes end, so if timed correctly it is fairly safe on grounded opponents. The biggest weakness is that every aerial has very long landing lag when they aren't autocanceled, so you cannot throw an attack out near the ground and expect it to save you against someone shielding or dodging. Throws are the easiest and best way to get Zard in the air, so characters that are naturally good at landing grabs are gonna give you trouble. Oh, and heyyyy, most of those characters are also really good at juggling! How about that? If you aren't sure of which characters I'm referring to, mosey on over to any fan-based tier list out there and take a peek at the top couple of tiers or so.
Characters that can pressure from far away with stuff like Sheik needles or Pika Jolt (lol both those characters apply to the first problem too) are also bad news because Charizard has very weak approach options. This is because of his aforementioned ****ty aerial game and fairly laggy grounded options. Flamethrower is pretty good, but if they can pressure you when you start to get in range of it, you have to really maneuver yourself well to use it, due to its startup. B-reversing, retreating short hop, etc. Dtilt got a minor buff at least.
The top tiers really have a field day with this character if they just play as campy lame as possible, but at least you live forever. If you can keep living forever, you can catch them with one of a number of kill moves that, with rage, will end stocks before 100%. But this is coming from someone who doesn't get to try the customs meta all that often, Dragon Rush and Rock Hurl and Fireball Cannon are really helpful for some matchups.
At least you can armor through stuff.