You must be a close relative of Colleen who is also researching Thomas VEETY (McVEETY) from Ireland. I see in a Google search for other message posts that Colleen thinks that her ancestor Thomas VEITY/VEETY was from Co. Cavan, Ireland, before settling in Pennsylvania. I hope you are exchanging information.
McVeety/Veety/Veity name variations that you and Colleen should check in Co. Cavan, or in fact anywhere in your Irish research, include:
MAC VITTY MACAVATY MAVITY MCAVITTY MCEVEETY MCEVEETY MCEVITY MCVEETY MCVEITY MCVITTY MCVITY MAC AVEETY MAC EVETEY MAC EVETY MAC VEETY MACAVEETY MAVEETY MAVETY MAVITTY MC AVEETY MC AVETTY MC AVETY MC AVITIE MC AVITTY MC AVITY MC EVEETY MC EVETTY MC EVETY MC EVITA MC EVITE MC EVITEY MC EVITY MC VEETEY MC VEETY MC VEITY MC VETEY MC VETTY MC VETY MC VITEE MC VITEY MC VITTEE MC VITTIE MC VITTY MC VITY VEETY VITTARY MAC VITTEE MAC VITY MACVITTY MACAVEITY MACAVETY MACAVITY MACVEATTY MACVEETY MACVEIGHTY MACVEITTY MACVITEY MACVITTIE MACVITY VEATY MCVITTIE MAC VEITY MC GIVITY MC VEITS MC VEYTI MC VINTY MCAVEETY MCVEATY MCVIETY MCVINGT MCVITED MCVITEE MAC AVITTY MAC VITTIE MAVIETY MC EVETEY MCAVATY MCAVEITY MCAVETY MCAVITY MCVEATTY MCVEIGHTY MCVEITTY MCVITEY MC AVATY MC AVEITY MC VEATTY MC VEIGHTY MC VEITTY MCVETTY MCAVETTY MCEVETY MCVITTEE MC VEATY.
The Irish Family History Foundation shows some records for McVeetys/Vettys in Co. Cavan, though it's not as numerous a surname as others. See http://cavan.rootsireland.iehttp://cavan.rootsireland.ie. And of course there were Protestant families of that name in Co. Monaghan (my area of research).
There were far more Catholic McVeetys in Co. Cavan than Protestant, and the 1901 census shows families of that surname and variations in more than one townland, and mostly Roman Catholic.
I don't see any Irish civil marriage registrations for Thomas Veety/McVeety (and variations) and Elizabeth Smith (and variations). If they were Catholic, if they married in Ireland 1864+, their marriage should be in civil registrations. If they were Protestant, their marriage could be in civil registrations much earlier (from 1845+). They may have married in England since Elizabeth was from that country; Thomas could have gone there to work and so met his bride and married her there.
Have you researched Michael Veety and William Veety who were living with Thomas Veety at the time of the 1870 census? And do you have Thomas' naturalization records? More biographical information might be in those papers.