It seems nobody has taken up the baton here, so I have spent some time digging into this.
When faced with a lack of parish register entries, as this case seems to be, the first thing I always look for are wills. they can be a mine of information.
Your Abraham Jesson died in 1777.
Have you got his will?
It is on findmypast (and lovely images they are too. Full colour instead of the grainy old black and white ones you get from other counties on there!).
He is a Tailor from Whitwick.
He has sons Abraham , John , William and George, plus daughters.
Rewind a hundred years, and there is another will for an Abraham Jesson, in 1678. He is a carpenter, and lives at ‘Swanyngton’ - Swannington, which is about 1 mile from Whitwick as the crow flies.
With such an unusal name, and so very close, there would seem a good possibility they were related.
Abraham in 1678 has sons Abraham and John , and daughters Mary, Sarah and Ann.
Son John is the executor.
Yet another will of an Abraham Jesson in 1734 also has him as a carpenter of Swannington. He is ‘aged and infirm’. Not hard to imagine he is the son of the Abraham in 1678,
(There is an ‘Abrm’ Gesson baptised 15.12.1654 of Abrm and Mary at Whitwick).
This Abraham of the 1734 will has sons Robert, John, Joseph, Benjamin, and daughter Katherine.
John is the executor and gets the residue of the estate.
(Perhaps this is the John of the other trees you’ve seen).
HOWEVER, there is a will of a John Jesson 1757, carpenter of Swannington, with brothers Robert and Benjamin, and sister Catherine, which would seem to be the son of Abraham of 1734. This John is a bachelor, and leaves his worldly goods to his brothers and sister and nephews - I didn’t see an Abraham Jesson mentioned, but that’s not to say he didn’t exist at that point in time - he may just not have had any bequest from John (or I may have missed it).
There are also wills for a Benjamin of Swannington in 1783, Robert Jesson in 1766, and a Catherine Jesson of Swannington 1765, amongst many others, which I have not looked at.
There does seem to be a dearth of baptisms and marriages for all these Jessons on the common research sites.
However, there are quite a few at Winwick listed under ‘Jeston’.
Thomas 1716 of Abraham and Elizabeth at Whitwick.
Elizabeth 1718 of Abraham and Elizabeth at Whitwick.
Sarah 1723 of Abraham and Elizabeth at Whitwick,
and John 1715 son of Abraham and Elizabeth - this is transcribed as ‘Jegson’, but in the actual register I’d say the ‘g’ is actually an ‘s’. It is also at at Whitwick
Plus others for different parents under ‘Jeston’.
If you say ‘Jesson’ and ‘Jeston’ quickly, you get pretty much the same word.
It may well be that there are other births etc in the registers, but the name has been transcribed as something that the research sites are not picking up as alternatives to Jesson. (I think I only found ‘Jeston’ as I did a search for any John born at Whitwick between certain dates. The sites don’t recognise it as a variation of ‘Jesson’.)
The registers are on findmypast, and are not too difficult to read. Depending on how many hours you have, and are prepared to take, I’d be wanting to go through all the pertinent pages for the dates I’d hope to find people.
There are many other Jesson wills for Leicerstershire - I was surprised how common the name was.
The ones I have looked at I scanned through pretty quickly - it would be well worth your while to look at them and trandcribe them properly - it’s not beyond the realms of possibilty that I’ve missed something.
If I were you, I would be combing many of these wills to see how the family all fitted together, and whether there is any mention of your Abraham in any of them. Possibly as a nephew or brother to another Jesson.
Perhaps draw up a family tree starting with Abraham in 1678, and fanning out with all the names from the wills in each generation so you can keep track of them all.
Lots of avenues for further research
Good luck!
And no, I couldn’t find a marriage for a John Jesson and a Frances Orton either.