late 14c., "person who pays," originally wages, later taxes (early 15c.), from Old French paiere (13c.), agent noun from paier (see pay (v.)).
"a payer, one who pays," by 1817, agent noun in Latin form from pay (v.). Chiefly legalese.
mid-15c., repaien, "pay back, refund," from Old French repaier, repaiier, "pay back, give in return," from re- "back" (see re-) + payer "to pay" (see pay (v.)).
The sense of "give (one thing) in return for (another)" is from 1550s; that of "make return, retribution, or requital for," in a good or bad sense is by 1590s. Related: Repaid; repaying; repayable.
c. 1200, paien, "to appease, pacify, satisfy, be to the liking of," from Old French paier "to pay, pay up" (12c., Modern French payer), from Latin pacare "to please, pacify, satisfy" (in Medieval Latin especially "satisfy a creditor"), literally "make peaceful," from pax (genitive pacis) "peace" (see peace).
The meaning "to give what is due for goods or services" arose in Medieval Latin and was attested in English by early 13c.; the sense of "please, pacify" died out in English by 1500. Figurative sense of "suffer, endure" (a punishment, etc.) is first recorded late 14c. Meaning "to give or render" with little or no sense of obligation (pay attention, pay respects, pay a compliment) is by 1580s. Meaning "be remunerative, be profitable, yield a suitable return or reward" is by 1812. Related: Paid; paying. To pay up was originally (mid-15c.) "make up the difference between two sums of money;" the sense of "pay fully or promptly" is by 1911. Pay television is attested by 1957.
early 15c., "estimated value or worth, proportional estimation according to some standard; monetary amount; a proportional part," from Old French rate "price, value" and directly from Medieval Latin rata (pars) "fixed (amount)," from Latin rata "fixed, settled," fem. past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").
Meaning "degree of speed" (properly ratio between distance and time) is attested from 1650s. Currency exchange sense of "basis of equivalence upon which one currency is exchanged for another" is recorded by 1727. Meaning "fixed public tax assessed on property for some local purpose" is by 1712.
First-rate, second-rate, etc. are 1640s, from British Navy division of ships into six classes based on size and strength. Phrase at any rate originally (1610s) meant "at any cost," hence "positively, assuredly." weakened sense of "at least" is attested by 1760. Rate-payer "one who is assessed and pays a local tax" is by 1825.