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St Mary's Stannington is not the same hospital as Ponteland hospital. There is a short history of Ponteland Hospital in "Pont Island News 2010" - the publication of Ponteland Local History Society - I'll post someting on the society blog.

The hospital started of as "The Work House" and as previous respondants have indicated it eventually became an "outpost" of Newcastle General hospital for elderly patients. 

There is a pedigree of Stephenson at................
http://www.robertstephensontrust.com/page10.html

George Stephenson (Famous Engineer) had one son Robert (famous engineer) who died childless. Robert was godfather of Robert stephenson Smyth Baden Powell (founder of Scout movement) - there were rumours that Robert may have been B-Ps father.

I suspect you will already realise that William Weallens was a family member and helped Henry get an apprentaceship at Robert Stephenson and company.

"The Rev. John Furness , of Ponteland, in 1822.  William Weallens was born, on the 8th of March, 1823 and subsequently received his education under Dr. Cowan, of the Grange, Bishopwearmouth .

His mother, who was widowed in 1828, subsequently married William Hutchinson who had joined Robert Stephenson and Co.  when the engine works was set up in 1823 and become works manager. It was probably Hutchinson who identified William’s potential as a mechanical engineer and enabled him to become a pupil of his stepfather on 3rd September 1838 apprenticed to Robert Stephenson and Co".

See ponthistsoc.freeuk.com - "Who was William Weallens"

Your 'ph' has turned into a 'v'

The 'ph' Stephensons were 'English' engineers mainly associated with 'Railways'
the 'v' Robert Stevenson was a Scottish lighthouse Engineer