My personal tactic for anvil droppers is to hold on to a speed boost. If you get hit with an anvil, fire it off and you're back up to speed in no time, giving them little time to use it to their advantage and catch up. Another one I use is to hold on to an anvil if I get it. If I'm in first place, and I get hit with one, I let mine go while I'm still flat and it smacks the guy behind me, giving me time to accelerate and nullify his advantage.
I have had people stink me for doing this, but hey, it's no different than holding on to an anvil to drop it on a guy just as he's about to win. Turnabout is fair play, and all's fair in love and war.

(or in this case, Toon Battles.

)
All in all, I find the anvils very frustrating myself, but people are going to use them and all you can do is find ways to fight back.