I'm not a big fan of the "big weapons" as a catch. In comparison, a bear will take less damage from a big gun than a regular mortal would. It would still hurt him, because it's a big weapon, but it does need to get through its thick skin, and because it is a ferocious animal, it can deal with the pain better as well.
Except that a high powered rifle or .45 magnum round will in fact punch through the thick skin etc without actually losing anything in killing power, that's what they're precisely designed to do (just as most military rounds can kill you through walls these days).
While it is true that it'll deal with pain and such better than the average person, I think the fact that most folks would stat up a bear with endurance in the 3-5 range instead of the typical human rating of 0-1 covers that sufficiently. Bear blubber really isn't as good as kevlar+strike plates against stuff designed to penetrate meat. Likewise a spear is actually a pretty effective weapon against an elephant if you know what you're doing with it. (I saw a video in college of a Pygmy running under an elephant, stabbing it once, running away and wait for it to die...)
If you want it to be more precise than the mechanical "weapon 3", I think you could represent the catch as "deep penetration weapons, such as spears, high powered rifles, pistol-3 magnum rounds". So the bear gets armor against a normal sword but not a heavy spear, against a shotgun, but not a rifle, against a flamethrower but not a tightly focused Fuego-blast (where Harry managed to control it properly and didn't dedicate any shifts to knockback) even though all of those are technically weapon 3+ attacks.
