The Simpson family.

Starting point.
Just to recap. Your direct line goes back :-
grandfather Richard Cooper + Ada Clapham
greatgrandfather Richard Cooper + Ellen Adcroft
greatgreatgrandfather Joseph Cooper + Mary Simpson

We are going to look at the family of Mary Simpson. What do we know about her? Well, she married Joseph in 1831 in Blackburn. And we know from the census she was born about 1811 in Darwen. Looking on the 1851 census there is only one Simpson family living in Darwen although there are plenty living in Blackburn.

Putting Mary Simpson 1811 in the familysearch site I found the following :
Turton (batch no. P005511)
Mary Simpson christened 20 Oct 1811
parents William Simpson and Ellen.
The parents match the family living in Darwen.

We will look at the 1851 census first because it gives information on birthplace.
Ho107,2261,209,18
Blackburn Darwen 2g
Highfield house.
William Simpson 63 Blacksmith born Gargrave Yorks.
Ellen Simpson 63 born Sharples Lancs.
Ruth Simpson 22 powerloom weaver born Over Darwen, Blacksnape
Jonathan Watson 18 grandson Blacksmith born Tottington

Mary's mother Ellen came from Sharples which is in the parish of Bolton Le Moors, today known simply as Bolton. Again on the familysearch site I found the following marriage.
Bolton Le Moors (Batch no M007151) St Peter
Willm. Simpson + Ellen Booth
26 Aug 1811.
[so Mary was christened less than two months later]

Looking on the Parish Clerk online site, for Turton St Anne Baptism
20 Oct 1811 Mary d. William+Ellen Simpson Darwen
So they were living in Darwen at that time.

What about Mary's father? Well he put Gargrave Yorks for his birthplace.
Again using the familysearch site I found:
Gargrave (Batch No. P007691, 1558-1812)
16 Sep 1787 William Simpson, parents Thomas and Mary Simpson

Possible siblings for William from this batch :
James Simpson c. 2 Apr 1786
John Simspon c. 16 May 1784
Molly Simpson c. 8 Dec 1782
Jane Simspon c. 1 Oct 1789

and a possible marriage for William's parents.
Gargrave (Batch No. M007691)
Thomas Simpson + Mary Crahe
2 Apr 1782

(also possibly Mally Craike c. 25 Mar 1757 Gargrave, parents John Craike +Margaret)
(possible marriage Gargrave 15 Jun 1756 John Craike + Margaret Cockshot)

possible brother of William 1851 census
H0107,2278,196,4
Skipton, Kettlewell 4b
Barnoldswick
Rock cottage?
James Simpson 65 Limestone quarryman employing 2 born Gargrave Yorks.
Jane 58
James 26 Limestone quarry labourer
Jane 24
Catherine 23
Thomas 20 Tin maker
Chester? 14

Whilst I would be quite happy to say that your greatgreatgreatgrandparents are
William Simpson + Ellen Booth, I would say that a lot more research in the Gargrave area would have to be done before confidently saying Thomas and Mary belonged to you. I have put the information on in case someone else from your family would like to investigate further. It would require looking at the parish registers for Gargrave in Yorkshire somewhere, and also researching the local history.

So we have Mary's parents, did she have any brothers and sisters?
Using the wonderful Parish Clerk Online, Mary's parents used Darwen Chapel, St James.
An outline of her family would be :-

William Simpson born 1787
Ellen Booth born 1788

Mary Simpson c. 20 Oct 1811
Betty Simpson c. 16 Jun 1813 - buried 5 Dec 1815
Peggy Simpson c. 27 Nov 1814
Anne Simpson c. 18 Aug 1816 - buried 18 Aug 1818
Betty Simson c. 26 Apr 1818
Thomas Simpson c. 29 Oct 1820 - buried 24 Aug 1824
Ellen Simson c. 27 Oct 1822
William Simpson c. 31 Jul 1825 - buried 18 Feb 1826
James Simpson c. 31 Dec 1826
Ruth Simpson c. 8 Mar 1829

This is the same Darwen Chapel that Mary and Joseph used for their children Betty and William (the records stop on the internet for this Chapel in 1836).