PROCESSION was a method of verifying the boundaries
of a person's property. The church appointed men to walk the
boundary lines of certain properties. Property lines being barely
discernable through swamp and brush, the men walked one behind the
other instead of side by side. Therefore, the term applied to the
walk was "procession". The concerned property owners or their
representatives were supposed to be there to point out the way and
the landmarks that defined the boundary. 

EX:
Processioned for Henry AVERIT in presents of James
MOOR  Henry AVERIT and William TURNER.


Note that the last two
listings below indicate that no one was present to show the
processioners where the lines were. This was during the time when
the church of each parish was basically responsible for much of the
law. In the case(s) you list, the order for PROCESSION was
given/made by the Vestry of Society Parish and since this was in
1770, it was definitely before the Revolution and in the time when
the Church of England was the controlling authority in the English
colonies.

EX:
Some part of Thomas BARKER Land not sd Jesse ?
nobody appeared to show  lines -  and William
Williams not appeared to show his lines and it was
lost?

Some part of a piece of land belonging to Mr. MEADE 
nobody appeared to show    the lines.