Does this help?

Basically, the idea is to have another column that counts the weeks between two dates.

--= test data

DECLARE @t table(theDate smalldatetime, FinYear smallint, FinPer tinyint, FinWeek tinyint) ;

set nocount on ;

insert @t values('2009-12-27', 2010, 1, 1) ;

insert @t values('2009-12-28', 2010, 1, 1) ;

insert @t values('2009-12-29', 2010, 1, 1) ;

insert @t values('2010-01-19', 2010, 1, 4) ;

insert @t values('2010-01-20', 2010, 1, 4) ;

insert @t values('2010-02-18', 2010, 2, 8) ;

insert @t values('2010-02-19', 2010, 2, 8) ;

insert @t values('2010-03-25', 2010, 3, 13) ;

insert @t values('2010-03-26', 2010, 3, 13) ;

insert @t values('2010-04-30', 2010, 4, 18) ;

insert @t values('2010-05-01', 2010, 4, 18) ;

insert @t values('2010-05-28', 2010, 5, 22) ;

insert @t values('2010-05-29', 2010, 5, 22) ;

insert @t values('2010-06-28', 2010, 7, 27) ;

insert @t values('2010-06-29', 2010, 7, 27) ;

insert @t values('2010-08-27', 2010, 8, 35) ;

insert @t values('2010-08-28', 2010, 8, 35) ;

insert @t values('2010-09-15', 2010, 9, 38) ;

insert @t values('2010-09-16', 2010, 9, 38) ;

insert @t values('2010-09-29', 2010, 10, 40) ;

insert @t values('2010-09-30', 2010, 10, 40) ;

insert @t values('2010-12-16', 2010, 12, 51) ;

insert @t values('2010-12-17', 2010, 12, 51) ;

insert @t values('2010-12-18', 2010, 12, 51) ;

insert @t values('2010-12-19', 2010, 12, 52) ;

insert @t values('2010-12-20', 2010, 12, 52) ;

insert @t values('2010-12-26', 2011, 1, 1) ;

insert @t values('2010-12-27', 2011, 1, 1) ;

insert @t values('2010-12-28', 2011, 1, 1) ;

insert @t values('2011-03-03', 2011, 3, 10) ;

insert @t values('2011-04-03', 2011, 4, 15) ;

insert @t values('2011-05-05', 2011, 5, 19) ;

insert @t values('2011-05-28', 2011, 5, 22) ;

insert @t values('2011-06-18', 2011, 6, 25) ;

insert @t values('2011-06-19', 2011, 6, 26) ;

insert @t values('2011-07-10', 2011, 7, 29) ;

insert @t values('2011-08-08', 2011, 8, 33) ;

insert @t values('2011-08-29', 2011, 9, 36) ;

insert @t values('2011-10-08', 2011, 10, 41) ;

insert @t values('2011-11-21', 2011, 11, 48) ;

insert @t values('2011-11-22', 2011, 11, 48) ;

insert @t values('2011-12-27', 2011, 12, 53) ;

insert @t values('2011-12-28', 2011, 12, 53) ;

insert @t values('2011-12-29', 2011, 12, 53) ;

insert @t values('2011-12-30', 2011, 12, 53) ;

insert @t values('2011-12-31', 2011, 12, 53) ;

--= sample for dates 2010-12-18 and 2011-12-31 -

--= unfortunately the answer is wrong because all dates are not present between, but the idea works

select max(WeekNum) from (select DENSE_RANK() OVER(ORDER BY FinYear,FinPer,FinWeek) as WeekNum

from @t

where theDate BETWEEN '2010-12-18' AND '2011-12-31') as a

You could add a column like this to the table itself and just pull the difference between the two values by date to save some io cost.