'expense' originates from Latin, specifically the word 'expensa' (from the past participle 'expensum'), where the prefix 'ex-' meant 'out' and the root 'pendere' meant 'to weigh' or 'to pay'.

'expense' moved into English via Old French 'expense' ( Medieval Latin/Old French), coming from Late Latin 'expensa' / Latin 'expensum'; it entered Middle English as forms like 'expence' and eventually became modern English 'expense'.

Initially it meant 'a payment or sums paid out' (that which is paid out); over time it broadened to mean both 'a cost or charge' and 'the act of incurring/recording that cost' as in modern usage.