Gaelic form of Martha.
A US correspondent [MB] reports that
"... throughout the southern colonies (pre 1776) and states, Patsy was a common pet name for Martha."
We are unable to formally determine the true etymology for this but note that Patty is a well-known pet name for the Gaelic Moireach, equivalent to Martha [Whyte]. Patsy is a clear variant of Pattie/Patty and we think it might have been adopted for Martha via the pet name Mattie/Matty in the same way that Molly has transformed to Polly].