The thing with Charzard that despite being a big character with horrible gliding, some of his moves can answer several of Meta's moves.
For example. His flamethrower can, as Shin said, stop an agressive Meta Knight. And as soon as it nears its exhaustion, you could maybe shield/powershield his attacks to punish with a grab or an fltilt.
His Rocksmash, answers Meta's specials. His forward B acts possibly just as fast or faster cause the moment Charizard is pulling his head back, the hitbox of the rocks is in place and if you get around that point, you're taking those hits. Meta's tornado would eat through it half the time to 1/4th. This is because not only his tornado can't take projectiles (yes, it's a projectile of sorts) over 12% of damage, but there's so many hitboxes hitting him at one time (this part is my theory though). As you saw, it can aswer to his Up B, which makes an effective edgeguard.
I don't see this as a counter to meta knight, but i also don't see this as a easy fight. A smart player can make up for some of PT's weaknesses.