Thomas Applegate II was known as Thomas Applegate "the weaver" and was listed as such in many records. He was married first to an unknown wife, and had his first 5 children; Thomas, John, Daniel, Joseph & Elizabeth. He then in 1678 married Joanna Gibbons the daughter of the Monmouth Patentee Richard Gibbons. Richard gave Thomas 100 acres possibly as a wedding present. The fact that Thomas divided this land in his will and gave it to his 2 youngest children is an indication that these children were of his second marriage to Joanna. 
Find A Grave, database and images (https://www.findagrave.com : accessed 01 June 2018), memorial page for Thomas Applegate, Jr (1632–Feb 1699), Find A Grave Memorial no. 45289797, citing Middletown Baptist Churchyard, Middletown, Monmouth County, New Jersey, USA ; Maintained by Sue McDuffe:) (contributor 47122067) .
It may be possible to confirm family relationships with Thomas by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: