On Robart's son Robart's christening record it says that Robart is from Nether Staveley, Westmoreland, which is 5 miles NW of Kendal.
Heversham where there is a possible christening record for Robart, senior, is 7 miles S of Kendal, but it's entirely possible that it's the same person as its only a 3.5 hour walk between the two locations.
Robart's parents might have been Robert Birkett and Mary Beeby from Troutbeck which is further NW past Windermere.