Old English lician "to please, be pleasing, be sufficient," from Proto-Germanic *likjan (source also of Old Norse lika, Old Saxon likon, Old Frisian likia, Dutch lijken "to suit," Old High German lihhen, Gothic leikan "to please"), from *lik- "body, form; like, same."
The sense development is unclear; perhaps "to be like" (see like (adj.)), thus, "to be suitable." Like (and dislike) originally were impersonal and the liking flowed the other way: "The music likes you not" ["The Two Gentlemen of Verona"]. The modern flow began to appear late 14c. (compare please). Related: Liked; liking.
<a href="https://www.etymonline.com/word/liking">Etymology of liking by etymonline</a>
Harper, D. (n.d.). Etymology of liking. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/liking