1530s, quaere "a question," from Latin quaere "to ask, inquire," "much used as a marginal note or memorandum to indicate a question or doubt, and hence taken as a noun" [Century Dictionary], second person singular imperative of quaerere "to seek, look for; strive, endeavor, strive to gain; ask, require, demand;" figuratively "seek mentally, seek to learn, make inquiry," probably ultimately from PIE root *kwo-, stem of relative and interrogative pronouns. Spelling Englished or altered c. 1600 by influence of inquiry. Compare quest.
Query stands for a question asked without force, a point about which one would like to be informed : the word is used with all degrees of weakness down to the mere expression of a doubt; as, I raised a query as to the strength of the bridge. [Century Dictionary]
"to question, ask questions; express doubt," 1650s, from query (n.). Intransitive sense is by 1680s. Related: Queried; querying.