In some situations, it makes sense to let the opponent know that if they so much as sneeze on someone you protect, it will cost them a limb. If you have tried an eye for an eye and it really didn't do anything except help sell eyepatches, the only way to stay alive is to be drastic. Pay back any offense tenfold, or even a hundredfold if necessary, until the survivors learn to stay away. It's a common tactic of militaries the world over, with some regimes (such as Nazi Germany) being infamous for it.
That said, the "Justice" these rivals have in mind is more akin to a brutal beatdown... well, most of the time it is an actual brutal No-Holds-Barred Beatdown, supposed to culminate in the receiver's humiliation or death. Any attempt to get them to see the (all too obvious) truth, show mercy, or realize they're a step away from utterly ruining the receiver's life/committing murder will never succeed. It invariably takes the hero beating the rival, be it in a Cooking Duel or Good Old Fisticuffs, and proving Right Makes Might for the poor deluded soul to realize they were wrong all along, sometimes even coming around and realizing that Defeat Means Friendship.
All too often, these guys refuse to see reason. They promise that they'll come back to kill the hero, and shove his "mercy" and offer of friendship down his wind pipe. It might take the arrival of a plot significant character to clear things up and hand out some Epiphany Therapy to all involved.
This is not limited to the antagonist's side. God help you if that hero you've harmed has a Poisonous Friend. And all parties to a masquerade, good or bad, are often required to kill any poor schmuck who accidentally sees something he's not supposed to.
Intriguingly, while disproportionate can possibly mean underdoing it, you'll almost never see that happen.
A Sister Trope to Felony Misdemeanor (treating a relatively harmless misdeed as if it were a serious crime), Misplaced Retribution (the punishment is inflicted on the wrong people), Law of Disproportionate Response (reacting to serious matters like they aren't that important and vice versa), Disproportionate Restitution (a means of apology doesn't come close to making up for what the person has done), Disproportionate Reward (a minor or major act of kindness is reacted to in this way), There Is No Kill Like Overkill (the avenger won't let up even after the victim has stopped breathing).
Compare Make an Example of Them (punishing someone to deter others), George Jetson Job Security (losing your job for a trivial reason or no reason at all), Revenge by Proxy (getting back at those who wronged you by murdering someone close to them), RevengeSVP (ruining parties and other social gatherings for not being invited to them), Shoplift and Die (shopkeepers killing anyone who tries to make off with their wares without paying), Irrational Hatred (having it in for someone when there's no rational reason to despise them), Cycle of Revenge (where two parties endlessly invoke Disproportionate Retribution toward each other), Berserk Button (something that causes someone to become extremely pissed off and likely cause them to dish out Disproportionate Retribution), Evil Is Petty (villains doing assholish and cruel things just because they can), Die for Our Ship (fans bash characters solely for interfering with their preferred shipping), and Ron the Death Eater (fans depict a character as crueler, more spiteful, and otherwise worse than they are in canon simply for not liking them). If the retribution is played for laughs, compare Comedic Sociopathy.
Contrast with Unishment (a punishment that isn't a punishment at all) and Restrained Revenge (paying back a slight with retribution that is less severe than what was intended before rather than forgive the person in question). Expect the character dishing this out to justify this no matter what anyone speaks against it. Expect someone (doesn't needs be the Only Sane Man) to be Disappointed by the Motive if the retribution is just that absurdly disproportional to the reason.
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If you don't like this stinger, it's time to RUN. The Navy SEALs are coming.