allowyoudaoicibaDictYouDict[allow 词源字典]
allow: [14] Allow comes ultimately from two completely different Latin verbs, allaudāre and allocāre, which became blended in Old French alouer. The first, allaudāre, was based on laudāre ‘praise’ (source of English laud, laudable, and laudatory); the second, allocāre (source of English allocate [17]) on locāre ‘place’.

The formal similarity of the Latin verbs gradually drew their meanings closer together. The notion of ‘placing’, and hence ‘allotting’ or ‘assigning’, developed via the now obsolete ‘place to somebody’s credit’ to ‘take into account, admit’. Meanwhile, the idea of ‘praising’ moved through ‘commending’ or ‘approving’ to ‘accepting as true or valid’, and ultimately to ‘permitting’.
=> allocate, laudable, location[allow etymology, allow origin, 英语词源]
allow (v.)youdaoicibaDictYouDict
early 14c., allouen, "to commend, praise; approve of, be pleased with; appreciate the value of;" also, "take into account or give credit for," also, in law and philosophy, "recognize, admit as valid" (a privilege, an excuse, a statement, etc.). From late 14c. as "sanction or permit; condone;" in business use from early 15c.

The Middle English word is from Anglo-French alouer, Old French aloer, alloiier (13c.) "allot, apportion, bestow, assign," from Latin allocare (see allocate). This word in Old French was confused and ultimately merged with aloer; alloer "to praise, commend," from Latin allaudare, adlaudare, compound of ad- "to" (see ad-) + laudare "to praise" (see laud). From the first word came the sense preserved in allowance as "money granted;" from the second came its meaning "permission based on approval."
Between the two primary significations there naturally arose a variety of uses blending them in the general idea of assign with approval, grant, concede a thing claimed or urged, admit a thing offered, permit, etc., etc. [OED].
Related: Allowed; allowing.