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SQL Server para contar cuántas veces aparece un valor entre múltiples rangos de fechas y compararlo con semanas anteriores

Creo que esto podría darte lo que estás buscando:

;WITH 
weekcounts AS (
    SELECT Time_Stamp, Emp_ID, [Balance], ROUND(CONVERT(FLOAT,[Balance]) / 60.0,2) AS [Hours], DATEPART(week, Time_Stamp) AS int_week FROM newSampleData
)

,counts AS (
    SELECT Emp_ID, int_week, 1 AS int_count
    FROM weekcounts
    WHERE ([Hours] >= 7.5)
    UNION ALL
    SELECT weekcounts.Emp_ID, weekcounts.int_week, 1 AS int_count
    FROM weekcounts
        INNER JOIN counts
            ON weekcounts.Emp_ID = counts.Emp_ID
            AND (weekcounts.int_week - 1) = counts.int_week
            AND ([Hours] >= 7.5)
)

,countsagg AS (
    SELECT Emp_ID, int_week, SUM(int_count) AS int_count
    FROM counts
    GROUP BY Emp_ID, int_week
)

SELECT Emp_ID, 
       ISNULL([29],0) AS [week 29],
       ISNULL([30],0) AS [week 30],
       ISNULL([31],0) AS [week 31],
       ISNULL([32],0) AS [week 32],
       ISNULL([33],0) AS [week 33] 
FROM countsagg
PIVOT (MAX(int_count) FOR int_week IN ([29],[30],[31],[32],[33])) piv

Además, si Balance es un varchar, está haciendo más conversiones de las necesarias en el código proporcionado. Esto dará el resultado por horas con menos código:

ROUND(CONVERT(FLOAT,[Balance]) / 60.0,2)