I have not been able as yet to make a contact with a John Calvert Jr. researcher.I will go ahead and give you what I know, then maybe one will e-mail to correct me.I just do not have all the children, nor birth and death dates.
Going backward from your William Hanson Calvert: His father was William Calvert of Belmont as you have seen in the 1850 census.
William Calvert of Belmont was the son of John Calvert Jr. and Esther (Hetty/Hester) Jones both originally from Mifflin Co., PA.
John Calvert Jr. was the son of John Calvert of Mifflin and probably from Chester Co., PA.
Sometime in the late 1790's, John Jr., and his two brothers, Job and Jacob, crossed over the mountains from Mifflin to Belmont Co.
Strong circumstantial evidence links the elder John Calvert of Mifflin to Chester Co. and the family of Thomas Calvert and Sarah Williamson.Now DNA links John of Mifflin and Isaac Calvert (my ancestor) who also has strong circumstantial ties to the same Chester family.
Of course, there is much more to this.My e-mail address is firstname.lastname@example.org, could you contact me?