I'd do this one of two ways. Since you're setting your start and end dates in your t-sql code, i wouldn't ask for parameters in the stored proc
Option 1
Create Procedure [Test] AS
DECLARE @StartDate varchar(10)
DECLARE @EndDate varchar(10)
Set @StartDate = '201620' --Define start YearWeek
Set @EndDate = (SELECT CAST(DATEPART(YEAR,getdate()) AS varchar(4)) + CAST(DATEPART(WEEK,getdate())-1 AS varchar(2)))
SELECT
*
FROM
(SELECT DISTINCT [YEAR],[WeekOfYear] FROM [dbo].[DimDate] WHERE [Year]+[WeekOfYear] BETWEEN @StartDate AND @EndDate ) dimd
LEFT JOIN [Schema].[Table1] qad ON (qad.[Year]+qad.[Week of the Year]) = (dimd.[Year]+dimd.WeekOfYear)
Option 2
Create Procedure [Test] @StartDate varchar(10),@EndDate varchar(10) AS
SELECT
*
FROM
(SELECT DISTINCT [YEAR],[WeekOfYear] FROM [dbo].[DimDate] WHERE [Year]+[WeekOfYear] BETWEEN @StartDate AND @EndDate ) dimd
LEFT JOIN [Schema].[Table1] qad ON (qad.[Year]+qad.[Week of the Year]) = (dimd.[Year]+dimd.WeekOfYear)
Then run exec test '2016-01-01','2016-01-25'