William born 1251 can not be son of Henry if he died before birth of William Stop using your Favorite Wikipedia and Stirnet Junk https://en.wikipedia.org/wiki/Henry_de_Baliol
also it is Known that Henry and Alexander are both of Cavers https://books.google.ca/books?id=WV-TM0HNgeoC&pg=PA61&lpg=P...
(Cavers Castle) is in Ayrshire Scotland, That suggests those 2 where born there, Cavers Castle was owned and built by the "Baliol Family" around 1200 see here http://www.scotclans.com/scotland/visit-scotland/scottish-castles/s...
That does not mean other family members where not born there Thomas was of Cavers also and this source does not list William as son of Henry http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=tibar...
this source list William as Brother to Alexander
https://books.google.ca/books?id=u15IAAAAYAAJ&pg=PA265&lpg=...
as well as the Scott's Hall Book and Makes sense as Alexanders wife is of Chilham that is in Kent and William is Ancestor of the Scott's of Kent so William had a reasons to go to Kent from Cavers, as the Scottish wars of independence would be one reason to leave Cavers as the Baliol's had to change there name's also or Die and William de Baliol dropped Baliol as last name becoming William Baliol le Scot or William le Scot ancestor of the Scott's of Kent and Alexanders son William being a Baillie starting long lines of Baillies.
i would like to point out that playing around with there Occupations is not needed to Distinguish one individual from another just over complicates sorting out who is who William is a prime example, his occupation should not be with his name for the sake of where he fits in the Family, People can have several occupations over there life time, i for example Worked for the Coast Guard, i have been a Fense installer, a Power Tool Repair Technician, now im a CWB Certified Welder and Overhead Crane Opperator this stuff is not Rocket Science.
Its because of all this Crap that i Previously disconnected William from my Long Line of Scott's because i disagree with Henry as being the Father of William born 1251 not to mention the death date for Henry being years not 9 months before Williams Birth year