The key, I think, for this family line is the given name "Jesse". It is a somewhat unusual name for the period. Using the parish transcriptions from the Hampshire Genealogical Society, I find only 16 references to the first name "Jesse" in all of Hampshire between 1537-1659 for ALL surnames --one of these being a Jess born about 1616 in East Meon, son of Thomas Aylline. This surname is likely a derivation of the surname AYLING. A John Aylline has two girls baptized in East Meon at about the same time.
There are only 37 "Jesse" for all of Hampshire between 1660-1751 for ALL surnames --only two of which is for an AYLING: Jesse, son of Jess, in Buriton in 1702. There is also Jesse and Margaret having a son William baptized in Petersfield in 26 Apr 1726. They also have a daughter Elizabeth in 1730. I suspect this Jess father is the Jess baptized in Buriton in 1702. This might have been a first marriage with Margaret. Then a second marriage to Sarah in Northhampshire with David Ayling (B. 1749) as their child. So I think it might be reasonable to assume that this unique name is passed down from father to son. Obviously, this is not 100% certain; a completely separate Ayling family might have heard the name and adopted it into their line, but the name is retained with Jesse's descendants right down to the present. This implies that the same "ownership" of the given name carried back into generations before Jesse (B. 1749). As noted above, on that basis I built that Jesse Ayling tree and incorporated it into the larger tree "John Ayling (B. abt 1540) of Petersfield Hampshire & descendants Family Tree" on ancestry.com.
If you are interested you can "check my math" via the all Hampshire parish transcriptions for AYLING (and derivations) that I have posted at
http://boards.ancestry.com/surnames.ayling/mb.ashx. I believe these message boards are accessible to anyone even if not an ancestry.com member. They come up in google searches, for example.
Another avenue to explore might be military movements/stations/regiments in Hertfordshire and Hampshire. I did have a quick look on the internet via various military records for Hertfordshire, but didn't come up with Jesse.
There are a number of descendants working this line. I will certainly let you know if I or they come up with anything further to confirm or change my guesses. I should say that David Ayling is not my direct ancestor. My folks were in the Stedham/Woolbeding area at the start of parish record keeping in the 1540's, but some of those folks owned land in Hampshire and some moved there in the 1600's (eg. John Ayling, founder of the Ayling clan of Liss, descends from John Aylyng D. 1546 of Terwick who, along with his brother Richard Ayling D. 1545, a burgess of Midhurst, founded the Ayling clan of Stedham/Woolbeding, Sussex).
I think the northwest Sussex and north east Hampshire lines all come together in Bramshott and Petersfield pre-record keeping. For example, the Court of Common Pleas has a John and Philip Aylyng of Bramshott suing for trespass a Richard Aylyng of Bramshott and a John Ayling of Terwick in 1516.The "trunk" of the tree probably goes back centuries before that. DNA would probably be the only way to confirm links. However, there was likely constant movement across the county lines. For example, the miller of Stedham, Sussex was a Michael Aylyng in 1460, so it is not a straigh line movement from Hampshire to Sussex.
My guess is that our ancestors were originally living on or around Hayling Island in Hampshire. The Island was reduced in size over the centuries due to climate change and erosion. Those living near there may have had to re-locate and used that geographical feature as a ancestral memory when providing surnames in the late 1200's. "I am John of Haying". The "H" could have been dropped due to local dialect. I go into this idea in more detail at
http://boards.ancestry.com/surnames.ayling/164/mb.ashx.
Chris Ayling