How did 'amerce' (at the mercy) mean 'punishment'?

[jet_leader1]

What semantic notions underlie "mercy" (in "amerce") 🡺 with "punishment"?

These senses feel like polar opposites to me! Mercy is the polar opposite of punishment! If a court mercies a defendant, then a court shall not punish a defendant. If a court punishes a defendant, then the court hasn't mercied the defendant.

Etymonline

"punishment by arbitrary or discretionary fine," 1215, earlier amercy, Anglo-French amercier "to fine," from merci "mercy, grace" (see mercy). The legal phrase estre a merci "to be at the mercy of" (a tribunal, etc.) was corrupted to estre amercié, a good example of how an adverbial phrase in legalese tends to become a verb (compare abandon).

OED

 

[Platytude]

Mercy itself also means punishment, but a reduced one (e.g., out of compassion).

 

[Glasguensis]

The sources you have quoted explain the derivation: it comes from « to be at the mercy of ». Someone who is being punished is at the mercy of the person punishing them.