gistfile1.cs

class MyClass {
  public DateTime Date;
  public string Name;
}

var list = new List<MyClass> {
  new MyClass { Date = new DateTime(2012, 02, 01), Name = "Week 1" },
  new MyClass { Date = new DateTime(2012, 02, 06), Name = "Week 2" },
  new MyClass { Date = new DateTime(2012, 02, 13), Name = "Week 3" },
};

var weekTicks = (Int64)10000000 * 7 * 24 * 60 * 60;   
var groupedByWeek = list.GroupBy(s => s.Date.Ticks / weekTicks).ToDictionary(s => new DateTime(s.Key * WeekTicks), s => s.Count());;