Green’s Dictionary of Slang

inescapably; absolutely, completely, unreservedly.

1834		Satirist (London) 5 Jan. 7/2: The debt will be right on strangled this year at all advance; and now I see in the horison our real independence.
1934		C.S. Johnson Shadow of the Plantation 194: ‘Two of my chillen die with ‘yellow thrash.’ I gived them thread salve made from yellow berries but they die right on.’ .
1953		T. Runyon In For Life 203: He was a policeman right on, but the best I’d run into.
2010		W.D. Myers Lockdown 132: He can’t walk at all. That is just right on sad because everybody wants to walk.