Weah, signed on loan from Paris Saint-Germain during the January window, believes that he and his team-mates conducted themselves with decorum and argued that the ruling body had erred in issuing the charges.
The USA striker believes it is wrong to single out Brown, whom he regards as a mentor.
“To be fair, I was kind of surprised with [the charges],” he claimed. “I didn’t feel we had any negative type of conduct. Things get heated; it’s a derby, that happens. The Celtic-Rangers game is like no other. It is a bit of chaos because the players are really passionate and that’s a good thing.
“But I feel like everyone was positive. Nobody got a red card and we kept it very clean. Now we’re really positive and moving forward.
“I didn’t see anything wrong with the way [Brown] acted [on Sunday]. He did everything he needed to do to get his team to win and that is what a captain does.
“My team-mates and I respect him to the fullest and look up to him. He is our leader. It’s a bit different for me because I had never been in a derby match but Scott Brown leads by example and he’s a positive figure for this team; he was the main reason we got the win.
“Was he wrong to celebrate? It’s a derby win and we’d been looking forward to this match.
“Coach Neil [Lennon] got us in the locker room and told us we had to go out there and give blood, sweat and tears. That’s what we did and I think it just showed the passion Scott Brown has for Celtic.
“If you think about it, everyone said he was done but he showed that he has years left in him and that he can still play at a high level.
“I was proud of him and, when he does things like that, it shows he is super passionate about the game and the club. I feel the fans should really appreciate him because he loves Celtic and that feeds off to the other players. We see how much it means to him and that’s amazing.”
Weah believes that Brown is the beating heart of the champions.
“Is Scott Brown a role model? 100 per cent!” he said. “You feel his presence in the team and in the dressing room and he’s a huge reason why this team has gone so far as he keeps pushing us.
“On the field you can hear him – he talks to me 24/7 on the field. If I’m doing well then he tells me: ‘Good job’ and, if I can improve on something, then he tells me that too but he’s always positive and is a real role model for me.
“I look up to him a lot and I think every player should be a Scott Brown. I haven’t had the chance to have the green lights on me at night yet but Scott Brown’s presence in the huddle is amazing.
“It’s his presence again before the game and he gets us pumped up so he’s a huge part of this team.”
Weah didn’t come off the bench against Rangers but the 19 year old followed Brown’s example by becoming involved in the rumpus at the final whistle.
“I saw players attacking Mikael [Lustig],” he said. “He’s like a brother to me now and the right thing to do was defend him.
“That’s what Scott Brown does best; fighting for his team-mates and fighting for his club and that’s rubbed off on me.”