Performance difference between < and <=

Not sure what version of TokuDB you are running, or what MySQL/MariaDB distribution, but there is an index condition pushdown bug that occurs on queries similar to the one you've provided. We are still waiting for a fix, the only current workaround is to disable ICP when running the problematic query.

Try running the query with ICP turned off. To disable it, issue the following command in the session just before running the query:

SET optimizer_switch='index_condition_pushdown=off';

And please report back success/failure, and the particular versions of TokuDB and MySQL/MariaDB.

(full disclosure, I'm an employee of Tokutek, makers of TokuDB)

Much more efficient to do this without having to go back and join to the periods table.

DECLARE @StartDate DATE, @EndDate DATE;

Select @StartDate = Min(StartDate), @EndDate = MAX(EndDate) 
from dbo.PeriodCalendar_Weeks pcw
where (pcw.Year = @Year and pcw.Period < @Period) 
  or  (pcw.Year = @Year and pcw.Period = @Period and pcw.Week <= @Week) 
  or (pcw.Year = @Year -1 and pcw.Period >= @Period);

SELECT 
  WeekEndDate = DATEADD(DAY, 6, DATEADD(WEEK, SalesWeek, @StartDate)), 
  Store, 
  DeliveryChargesTotal = dct
FROM 
(
  SELECT DATEDIFF(DAY, @StartDate, SalesDate)/7, Store, SUM(DeliveryChargesTotal)
  FROM dbo.Daily_GC_Headers
  WHERE SalesDate BETWEEN @StartDate AND @EndDate AND isCanceled = 0
  GROUP BY DATEDIFF(DAY, @StartDate, SalesDate)/7, Store
) AS x (SalesWeek, Store, dct)
ORDER BY WeekEndDate, Store;

A filtered index may help, if many rows exist where isCanceled = 1 (these are just possible suggestions, depending on cardinality of Store, and may not be the most optimal):

CREATE INDEX x ON dbo.Daily_GC_Headers
  (SalesDate) INCLUDE (Store, DeliveryChargesTotal)
  WHERE isCanceled = 0;

If there are very few rows where isCanceled = 1, this may be better:

CREATE INDEX x ON dbo.Daily_GC_Headers
  (SalesDate, IsCanceled) INCLUDE (Store, DeliveryChargesTotal);

Both are worth trying on a test system, as well as moving Store into the key in either case, or moving IsCanceled to the INCLUDE list in the latter case. On my system, I found the best results with everything but the date in the INCLUDE list:

CREATE INDEX x ON dbo.Daily_GC_Headers
  (SalesDate) INCLUDE (Store, IsCanceled, DeliveryChargesTotal);

Again, you will need to test if any of these work out, or if the query above gives a different/better recommendation directly from SQL Server.