True to my word. A lesson in keeping it simple I think.

SELECT Sum_count = sum(Person_count), Aggregated_area
  INTO #tmp_B
  FROM Geo_postaggregated_pop_count
 GROUP BY Aggregated_area;


 UPDATE Geo_postaggregated_pop_count
   SET Sum_of_person_count = t.Sum_count
   FROM Geo_postaggregated_pop_count G
     , #tmp_B t
 WHERE G.Aggregated_area = t.Aggregated_area
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