PVD definitely counts for the Patriots - Foxboro Stadium is halfway between Boston and Providence, though I think Logan is probably the closer airport in distance, since T.F. Green is in Warwick, SE of Providence. It's probably a quicker drive from PVD than from Logan, though, due to the usually grinding traffic on Boston's Central Artery and SE Depressway.
Southwest makes it in MHT because they get traffic from Concord, NH (15 miles), Nashua, NH (15 miles), Portsmouth, NH (25 or 30 miles), and the many Boston suburbs/satellite cities (Lowell, Lawrence, Haverhill) along the NH border. Not to mention people willing to drive from southern Maine or Vermont. Southern NH has roughly one million people, and MHT can reasonably draw from another million in Massachusetts along the border for whom MHT is closer than Logan.
I'm not sure Green Bay would have the demographics for it, especially if they served MKE. Then again, Southwest does very well in smaller cities like Lubbock, Amarillo, Midland, etc.