Without doubt there is an historical concentration of this class of surname in Nottinghamshire, England (with a scattering in the surrounding counties). Using the early 19th century censuses as a guide we can examine the likely and/or possible surname variants/orthographies in the region:
Pailing
Palin
Paling
Payling
Pauling
Peeling
Pellinger
Pellington
As the spelling may be determined by the enumerators, one should check if it is consistent between each census. Examination of a few random samples shows that it isn't. That said it does seem that Payling is more consistent around Newark-upon-Trent but given the low numbers involved this may not be significant. The DNA evidence thus far shows that the Paling and Payling familes are one-and-the-same.
My prima facie suspicion is that in Nottinghamshire this name is not Welsh in origin (i.e. not Palin) as there are just too many variants and that the persistent "ing" ending is more indicitive of an Old English convention - meaning "peoples of" or "place of". In other words, in this area Paling mutated into Palin. It isn't clear (to me) if Pellinger / Pellington is connected but I mention them for sake of completion. If the surname class is toponymic then one might expect a number of distinct biological lines. We shall see.
Did they originate from this county or have they migrated from somewhere else? There are 16th century records of people called Pallinge in the adjacent county of Lincolnshire from roughly coastal locations - this could tie in with the Palling of Norfolk theory.
Here is a list of relevant Nottinghamshire habitation places (primarily for the benefit of the search engines):
Arnold, Bingham, Blyth, Burton Lodge, Farnsfield, Greasley, Halloughton, Holme, Hucknall Torkard, Lambley, Lowdham, Marnham, Newark Upon Trent, North Clifton, North Muskham, Orston, Oxton, Radcliffe On Trent, Radford, Rolleston, South Collingham, Southwell, St Mary, St Nicholas, St Peter, Strelley, Trowell, Upton, West Retford, Weston, Whatton, Wollaton and Worksop.
Other English Counties:
Palin Family - Cheshire (Susan Marlow's site)
External Sites: