I find acquittal or setting free [from guilt] to fit every usage in the New Testament, of which there are 17 (of which 10 are used by St. Luke), except for one in in Luke 4:18, but it falls into the category of a generic release or relief from a situation (which definition also fits well non-personal subjects), not a more personal ('forgiveness'); 'forgive' or 'acquit' being a more implicit nuance to the more literal meaning.

That is, 'release' would work for all uses (the "subsidiary" uses being injured somewhat by the literalness, though, in which cases 'forgive' is usually used).

As to its derivation, it is said to be derived from apo ([away] from) heimi (send, put), hence ἀφίημι (send away).

Our English 'forgive' is actually of a similar etymology, in that the Old English forgiefan, derived from 'for' (away, opposite, completely) and 'geifan' (give [up, away]). That is, take away the need or exercising of just exactment on someone or something for a crime or debt. And in the case of a captive, send them free from whence someone else had imprisoned them; or in the case of a non-personal entity, to issue forth or release to empty/clear out from.

Somewhere in the deep past, φημί may underly the word, in which ἀφίημι could simply mean to 'un-assert [the guilt of]' 'not-convict [of some crime or debt]'. Thus, acquit or set free from some form of exaction or other.

I find acquittal or setting free [from guilt] to fit every usage in the New Testament, of which there are 17 (of which 10 are used by St. Luke), except for one in in Luke 4:18, but it falls into the category of a generic release or relief from a situation (which definition also fits well non-personal subjects), not a more personal ('forgiveness'); 'forgive' or 'acquit' being a more implicit nuance to the more literal meaning.

That is, 'release' would work for all uses (the "subsidiary" uses being injured somewhat by the literalness, though, in which cases 'forgive' is usually used).

As to its derivation, it is said to be derived from apo ([away] from) heimi (send, put), hence ἀφίημι (send away).

Our English 'forgive' is actually of a similar etymology, in that the Old English forgiefan, derived from 'for' (away, opposite, completely) and 'geifan' (give [up, away]). That is, take away the need or exercising of just exactment on someone or something for a crime or debt. And in the case of a captive, send them free from whence someone else had imprisoned them; or in the case of a non-personal entity, to issue forth or release to empty/clear out from.

Thus, acquit or set free from some form of debt, obligation, sin, crime. In short, forgive.