We have found a Bridget Hennessy referred to on the gravestone marrying a Jeremiah Dwyer then moving to Bansha and subsequently having their children there. I think that marriage has been linked to.
I don't think we have found a death in Ireland for Bridget Hennessy Dwyer or emigration yet.
Bridget Hennessy Welch/Walsh dies in Westfield and is buried in Manchester.
Collating evidence + some sources for Jeremiah Dwyer & Bridget (Hennessy).
Marriage 21st Feb. 1846. No residence or parents' names in register. Link to register in Shanreagh's reply #64.
Children in birth order with baptism dates:
Bridget 19th January 1847 (Link in shanreagh's reply #74)
William 16th March 1848, sponsors John Dwyer & Joanna Walsh
Thomas 15th Sep. 1851, sponsors Jer. O'Leary & Mary Qu.....
Michael 5th June 1854, sponsors Laurence Hennessy & Cath. ___ (Link reply #74)
Kate 11th March 1856, sponsors John & Ellen Hennessy
Laurence 12th June 1858, sponsors John Dwyer & Cath. Whitstone
Alice 19th March 1862, sponsors John Merrick & Margaret Ga... (possibly Galvin)
Alice is the last child of the marriage we've found so far. If there were births 1864 or later they could be cross-checked with baptisms to establish residence/townland.
Judging by the births, it seems to me that Jer & Bridget Dwyer remained in the parish from their wedding and for most of 1850s and were still there in 1861/2. I doubt if either of them emigrated.
Among Jeremiah Dwyer entries in Tipperary on Griffiths' Valuation was 1 in Ballough townland, civil parish Templeneiry. I concentrated on that because a Bridget Dwyer of Ballough was daughter of a Jeremiah Dwyer, marriage 1889 to William Sampson (reply #64). Jeremy Dwyer occupied a house, offices and 32 acres of land. Michael Dwyer and William Dwyer were also occupiers in the townland. There were 787 acres in the townland, divided into 21 holdings.
Marriages of children of Jeremiah Dwyer:
Bridget to William Sampson 1889. Bridget's residence was Ballough. (Link reply #64)
Thomas 1889 (This wife died a year later after birth of their only child.) 1899 to a Dwyer bride. (Replies #79 & 80) A witness to one marriage was Alice O'Dwyer. Jeremiah was alive in 1889 as per marriage registrations.
Death registrations:
Bridget Dwyer 1873 Tipperary SRD, Bansha Reg. District. Farmer's wife, died at Ballough, age 52. (Reply #82)
Jeremiah Dwyer 1893 Tipperary SRD, Bansha Reg. District. Died at Ballough. Widowed farmer, age 85. Informant son Thomas. (Reply #78)
Thomas Dwyer, Jeremiah's son, remained at Ballough and was there for 1901 & 1911 censuses. There were other Dwyer households there, some headed by widows.
This is so far only conjecture that the Jeremiah Dwyer who married Bridget Hennessy was the same Jeremiah who lived and died at Ballough. It's also conjecture that the Bridget Dwyer who died in 1873 in Ballough townland was the wife of Jeremiah.
Summing up:
There is no firm (i.e. primary written) evidence from the above that the Bridget Hennessy who married Jeremiah Dwyer was the daughter of Thomas Hennessy of Lisvarranne as neither names of fathers nor residences of groom or bride were noted in the church marriage register.
However names of some of Bridget & Jer's children (Bridget, Thomas, Laurence, Alice) were same as some members of Thomas & Bridget Hennessy family. A baptism sponsor was Laurence Hennessy. (Caveat, Laurence may have been a common name locally.)
Jer & Bridget Dwyer seem to have remained in Tipperary after their marriage and for most of 1850s. It's unlikely that they went to U.S. Bridget was still in Tipperary in 1862 (baptism of Alice).
If Jeremiah, husband of Bridget Hennessy, was the same Jeremiah who lived in Ballough townland, he died there in 1893. If it was the same Jeremiah, Bridget may have died there in 1873.