1. If your game's setting allows for ridiculous sizes, then don't fight it. If your game has anime, action movie, or comic book inspired themes, let your players have those large weapons without fuss. These settings have large weapons all over in their episodes and issues, and it doesn't make any sense to deny players access to them, especially when it heightens enjoyment of the game. As always, players should at least have a reason why their knight has an oversized great sword, or their power armor should have a giant cannon mounted on it's back. It's just extra flavor and builds connection to the character they play.
2. Speed it up! If your game DOES have huge cannons and massive damages, don't slog your game by rolling more dice. Roll less whenever possible. Figure out a system of multipliers when more than three dice are involved. (example: 3d6x10, or 1d8x4). Yes, its funny to think that your character's laser sword does 60d10 damage with each successful hit. But when it comes to keeping the pace of your game exciting, that's a sure fire way to kill the mood. To establish the devastating power of the weapon, try NOT rolling dice. Have that giant gun just vaporize its target (with good description, of course) if you feel it does that kind of damage anyway. This will build a sense of just what the character has in his/her hands, and create some great dramatic moments for your story.
3. It works both ways. If the characters get big guns, then so do your enemies. Surprise the player characters by having them face an opponent with equal firepower. If the players have a warship equipped with ballistas, then have them face another ship with some ballistas. This establishes the scale within which they work. It's not about keeping them low on the food chain, it's about keeping the food chain moving so they don't become complacent at the top. This also helps prevent the game from becoming unbalanced on one side because the players shouldn't need to feel overwhelmed or underwhelmed by their opposition. If the players want a big scale battle, then facilitate that.
Bonus XP: Macross, Voltron, and Invader ZIM are fine examples of television shows that feature oversized weapons. Final Fantasy VII, Wild Arms, and Front Mission are great video games to explore themes featuring large guns and large-scale warfare. The Iron Man, Hellboy, and any title featuring the character Lobo are excellent comics for researching giant weapons and big explosions.