The 3rd PA Co 3 might refer to a called-up unit.The Roach article infers the PA militia units which were called up using the officers; names and the "class" designation based on the 1778 after-the-fact militia returns.
All the Northampton militia units were called up in 1777.The term of militia enrollment was three years.A major point to consider is that the officers of a company and the brigade did not necessarily get called up with thier fellow militia on the roster.The Roach book has a chart describing which officers were to go with which units according to the Militia Act of 1777.
I am still working through the fascinating Roach article to determine when and where my ancestors were in 1777.That time frame covers rushing to confront Howe as he sailed from NY to launch a major attack (which eventually was revealed to be Phila).Brandywine and Germantown were in that campaign.But most probably the Northampton 3rd Co just missed Germantown and spent the beginning of the 1777-8 winter near the crossroad of Old York Rd and Bristol Rd in Warwick & Warrington Townships in Bucks County, PA -- just four miles from my home. While the Continental Army settled in to "comfortable" quarters and were supplied with food during that winter at Valley Forge, PA militia units (including Northampton) were blocading the major roads into Phila and foraging for shelter and food wherever they could find it.
Although I have not found any evidence yet, there is a possibility that Northampton militia may have joined the Continental Army after it broke camp at VAlley Forge and traveled over through New Hope (probably roughly following present day Rt 202) on the way to the 2nd American victory (Washington's first) at Monmouth, nj.(Saratoga was the 1st vistory).Trenton & Princeton in 1776 were more properly called skirmishes.
In conclusion, focus your reading on the Roach article for clues in your search.