What is the history of using "Jersey" for "New Jersey"?

I have long wondered the origin of calling New Jersey by the nickname "Jersey". To the best of my knowledge, no one has ever shortened New York or New Hampshire to "York" or "Hampshire", or referred to the New England Region as "England".

Unfortunately, in the past I have gotten some ridiculous answers to this ranging from... "it just sounds right", to... well, York is in "England"....

Hint: 1) it "sounds right because you have heard it often enough", 2) All the locations with "New" in front of them are already locations in the UK, that is why we prefix it with "New".

I am hoping this question generates a thoughtful response, as opposed to 5th grade NJ jokes. My answer so far, (that I made up) is it may all boil down to one farmer’s sign, somewhere in NJ, where he advertised "Jersey Tomatoes" , ( or some such billboard,) and it was seen by enough motorists that it stuck. But I welcome any intelligent income from such an esteemed bunch of readers.

Referring to New Jersey simply as “Jersey” dates to at least 1705:

Elizabeth-Town in Jersey, Aug. 30. On Monday the 20 Currant, Dyed here in the Afternoon the Reverend Mr. John Harriman, Pastor of the Church in this place, Aged about 60 Years : Who the same day at a Church-Meeting told his people, that his time of departure drew near, and exhorted them to Peace and Unity one with another, and to stand fast in the Covenant that they had engaged themselves to. — The Boston News-Letter, Sept. 3–10, 1705.

Canterbury (in Connecticut) July 3. On Monday last Died here our Excellent Pastor, the Reverend Mr. Samuel Estabrooke, … he was invited to Preach the Gospel at East-Jersey, where he was highly respected and very serviceable for several years ; but having a strong Affection to New England, he never fix'd at Jersey, but chose to return to his Native Country ; — The Weekly News- Letter, July 6-13, 1727.

To be SOLD, By John Snowden, Tanner, 450 Acres of Land on a Branch of Rariton, called Black River, in Jersey ; and near 200 Acres further up in the last Indian pur chase, and Two Acres and a Half joining to Judge Leonard's Land in Princetown near the Tavern. — The Pennsylvania Gazette, Feb. 11-18, 1734-5.

The adjective did not have to wait for roadside vegetable stands:

Ran-away the 19th of this Instant August from William Hirst, of Salem Esqr. a Jersey Boy, Named John Amy about 15 years of Age, well Sett, full Leggs, short brown Hair, Ozenbrigs Jacket and Breeches, Cotton & Linen Shirt, a Cap on his head, bare-foot and bare leg'd. — The Boston Nexus-Letter, Numb. 488, from Mond. Aug. 17, to Mond. Aug. 24, 1713.

Often, there was not just one “Jersey”:

Philadelphia, Jan. 26. We hear from Burlington, that on Tuesday the 19th of this Instant, a Marriage was consummated between Edward Peitce, Esq ; Attorney Generall of the Jersies, and Mrs. Catherine Talbot, Widow of Mr. Robert Talbot, deceased : A Lady of great Merit. — The Pennsylvania Gazette, January 19-26, 1730-31.

Inhabitants of the Jerfies, men, women, and children are reckoned at about 50,000, whereof 10,000 may be reckoned a training militia. — William Douglass, A summary, historical and political, of the first planting, progressive improvements, and present state of the British settlements in North-America, Boston/London 1755.

A tax list further divides the colony into two parts: from 1674—1702, the East and West “Jersies” were under different provincial governments. Counties in the “East Jersies” were Somerset, Monmouth, Middlesex, Essex, Bergen; “West Jersies” were Cape May, Salem, Gloucester, Burlington, and Hunterdon. Morris and Trent were recently formed and had no tax information. The complete title of Douglass’ book includes “the history of the provinces and colonies of New-Hampshire, Rhode-Island, Connecticut, New-York, New-Jersies, Pennsylvania, Maryland and Virginia.”

In 1835, John James Audubon still uses a plural, though with corrected orthography:

In the Jerseys I have found the Night Herons breeding on water oaks and cedars…

Following up on KarlG's informative answer, I note an occurrence of unadorned "Jersey" in reference to the colony of New Jersey (or East New Jersey) in a letter from Gavin Laury to a friend in London, England, dated March 26, 1684, reprinted in The Model of the Government of the Province of East-New-Jersey in America (1685):

East-Jersey, March 26. 1684.

Loving Fiend,

I Promised to write to thee when GOD brought me to Jersey, but had not time till now, I shall give thee a breef, account of the Countrey, no fiction but the truth; It is beyond what I expeċied, It is scituate in a good Aire, which makes it healthy; and there is great conveniency for travelling from places throw the Province in Boats, from small Canoa to Vessels of 30, 40, or 50, Tun, an in some places 100; In the Bay coming up to Amboy point, where the town of Perth is now in building, a ship of 300. Tun may asily ride closs to the Shoar, within a plank length to the Shoar, ...

The reference is to what is now the city Perth-Amboy, New Jersey.

And likewise, from a letter from William Penn to the Commissioners of Propriety (of Pennsylvania) dated April 14, 1689, reprinted in The Papers of William Penn, Volume 3: 1685-1700 (1981):

I would have the business of my Island of Cepassin ended with Mr Biddle who planted it against caution on the side of Jersey: and Pennsilvania Govermt has had a great sweat out of it: and it never belonged to the land of t'other side among the Indians. So that it is by grant from the Crown, and by Indian purchase of those that had the title, mine.

...

I am much troubled there is no entertaynmt for servants out of their time, as ought to be; by which means they are forced to Jersey & else where. We have lost some hundreds of inhabitants by those insufferable tracts of Land that are un-seated wch drive new comers so uncomfortably back, that they declyne the Province for it, quite contrary to the very end of my first having to do with the Province: Do, I pray, what you can herein, till a tract be set apart for servants out of their own time, that may be called Freeman-town, or Freetown.

Penn seems comfortable with referring to New Jersey as "Jersey," since he does so twice in this letter.