If we consider a weakness' strength based on how many actions it takes to get rid of, Tommy Malloy is pretty harsh. His ability basically requires your team to spend three actions, minimum, to off him, which is more than most weaknesses.
There's also very few ways to mitigate the action sink, especially at level 0: you can use one-two punch to get 2 damage in one action, but you just played an event that normally does 4 damage for 2. The other option is Beat Cop, who you'd rather keep around as long as possible. Combine both and you can do it in one action, but you just spent six resources, static +1 combat, some soak and your most damaging event to remove a weakness. I'd rather just blow a whole turn taking basic fight actions, since Tommy's crummy fight stat makes him easy to hit.
In multiplayer someone could evade him, but solo that's really not an option. Even then, someone has to deal with him eventually, eating up your team's actions.
In short, he's really annoying, and will probably take three or more actions to get rid of. At least you can play Glory when you kill him.