First of all I would take a look at all the Eccles in Ayrshire in the 1841 Census using FreeCEN and get an idea of who is in what household (there are only about 50 Eccles). The main groupings are at farms and smallholdings near Ayr (Content, Corton, Burnton and Masonhill).
There were three Eccles brothers: John, Alexander and Gilbert. From baptism records, Gilbert was born 28 January 1762 to Alexander Eccles and Marion McIlmorrow [OPR Colmonell]. They also had a daughter baptised Margaret in 1764. You need to look at wills and testaments to get the real detail.
Neither John nor Alexander seems to have had surviving children and it appears they feued portions of property. John Eccles of Content died 6th Jan 1824 [SC6/44/1 Ayr Sheriff Court]. Alexander Eccles died in September 1842; he drew up a settlement on 3rd July 1833 and added a codicil on 27th October 1837 [1846 SC6/44/14 Ayr Sheriff Court]. These documents mention many Eccles nephews and nieces (and helpfully spouses of nieces). I will leave you to unravel these. Gilbert Eccles did not leave a will as far as I can see, but his youngest son Robert did [1867 SC6/46/5 Ayr Sheriff Court].
Happy hunting, Kay (Edinburgh).