While weapons are geared towards the Heels, only certain ones will actually show up armed with one. And while Babyfaces can use weapons, the mechanics of the game are designed to discourage this practice. Any use of a weapon in a match is regarded as a "cheap shot". While hitting your opponent with a weapon is a good way of rapidly building up their Humilation, it comes at the cost of increasing your "Foul" stats, and will quickly make Babyfaces unpopular with the audience (since it's considered unsportmanslike behaviour). The audience will express their dissaproval of this by boeing the player.
Here is a list of Weapons that appear in the games: