interest: [15] The Latin verb interesse meant literally ‘be between’ (it was a compound of inter ‘between’ and esse ‘be’). It was used metaphorically for ‘be of concern, be important, matter’, and appears to have been borrowed into Anglo-Norman as a noun, meaning ‘what one has a legal concern in or share of’. English took this over in the 14th century as interesse, but it gradually changed over the next hundred years or so into interest, mainly due to the influence of Old French interest ‘damage’, which came from the third person present singular form of the Latin verb.
The main modern sense ‘curiosity’ developed towards the end of the 18th century. [interest etymology, interest origin, 英语词源]