What is the origin of "GO + VERB + ING"?

Solution 1:

The origin goes back to Old English, as far as the year 1000 or earlier (according to OED). OED gives OE (Old English) for the date section of the two earliest citations.

Definition:

With participle indicating a concomitant action or activity.

Earliest citation:

Þa eodon hi sprecende ymbe þæs hælendes þrowunge him betwynan.

Ælfric of Eynsham, Catholic Homilies

Other examples in chronological order are: (OED)

  • eodon biddende, OE
  • eode singuynde, c1300
  • go wryȝinge, c1380
  • go hippinge, c1430
  • go walkyng, 1483
  • went preachyng, a1535
  • wente askyng & serchyng, 1548
  • go begging, 1615
  • went looking about, 1658
  • Went prancing, 1719
  • went mumping, 1775
  • went dancing, 1841
  • went sailing, 1895
  • went rushing down, 1930
  • went sprawling, 1988
  • went sniffing, 2013

OED mentions that the above definition is the formally similar sense of the following definition:

intr. To move, travel, or proceed (to somewhere) so as to perform a specified action, or for the purpose of a specified or implied activity.

    f. With verbal noun or gerund.

        (b) Without prefixed particle.

The earliest citation is from a1500:

Euery-on an hauke on honde ber, & went haukyng [c1330 Auch. riden on haukin] by þe ryuer.

Sir Orfeo, Harley

Other examples in chronological order are: (OED)

  • went hunting, 1658
  • have gone hunting and hawking, 1672
  • go Hunting or Hawking, 1707
  • go shooting of Birds, 1749
  • goes gunning , 1846
  • went gambling, 1861
  • ‘go clamming’, 1887
  • went automobiling, 1915
  • went fishing, 1933
  • going camping, 1960
  • go clubbing, 2003

OED also gives:

(a) With prefixed a (also †on) Now arch. and regional.

The earliest citation is from c1300:

Þis child scholde wende An hontingue.

St. Kenelm (Laud) 148 in C. Horstmann Early S.-Eng. Legendary

Conclusion:

It looks like this construction was first being used for actions, and then extended to activities. In OED, the earliest example with an outdoor activity is "go walking" (if we exclude the constructions with prefixed a). Then, we start seeing examples like "go hunting" starting from 1500s as sport-like activities. Although, the earlier form is with prefixed a. (go a hunting).

We are more familiar with this construction for sports and outdoor activities but it can be used with other leisure and indoor activities like bowling, shopping, dancing, clubbing etc.

Solution 2:

“To go hunting” derives from an older form such as to go a-hunting. Wiktionary has an article on this a-gerund under the headline a- -ing.

Wiktionary says this prefix a- was the form on. I'm not so sure. Theoretically this prefix might derive from various prepositions at, to, on, in. Originally the word formation was a- + gerund with the unambiguous ending -ing(e), Old English -ung/-ing. Later on, when the original ending of the present participle changed from ende over inde to inge both endings developed the same form and today, at least in most textbooks, these forms are seen as participles, though gerund would make more sense, as such forms are parallel to German

  • Wir gingen zum Jagen—literally: "We went to the hunting".

Later this prefix was no longer used except in some dialects and in poetry where an archaic effect is sought.

Solution 3:

First noted?
Gone fishing and Gone fishin' are in use as far back as the NGram goes.

...and here's the King James Bible (1611) for John 21:3

Simon Peter saith vnto them, I goe a fishing. They say vnto him, Wee also goe with thee. They went foorth and entred into a ship immediatly, and that night they caught nothing.

translating ‘Υπάγω ‘αλιέυειν vb + infinitive vb 'I-go to-fish.