Aggregating data in .net SQL
For Close, you can use the LAST_VALUE window function to get the last value from a data set (assuming this is the Close value from the last day of the week). You can then put this in an inner select statement and do a simple aggregation on the outer statement to return your intended results.

LAST_VALUE

Note, the below example assumes a last day of the week as Saturday. If this is a different day, look at using SET DATEFIRST to set your preferred day of the week as the start.

Setup:

CREATE TABLE #DailyTable (DateLogged DATETIME,
    High DECIMAL(10,2),
    Low DECIMAL(10,2),
    [Close] DECIMAL(10,2)
)

INSERT INTO #DailyTable (DateLogged, High, Low, [Close])
VALUES ('2019-05-31 00:00:00.000', 2.12, 1.06, 1.59)
,('2019-06-01 00:00:00.000', 2.44, 1.22, 1.83)
,('2019-06-02 00:00:00.000', 0.84, 0.42, 0.63)
,('2019-06-03 00:00:00.000', 0.84, 0.42, 0.63)
,('2019-06-04 00:00:00.000', 1.24, 0.62, 0.93)
,('2019-06-05 00:00:00.000', 1.12, 0.56, 0.84)
,('2019-06-06 00:00:00.000', 0.16, 0.08, 0.12)
,('2019-06-07 00:00:00.000', 3.00, 1.50, 2.25)
,('2019-06-08 00:00:00.000', 3.52, 1.76, 2.64)
,('2019-06-09 00:00:00.000', 3.40, 1.70, 2.55)
,('2019-06-10 00:00:00.000', 3.36, 1.68, 2.52)
,('2019-06-11 00:00:00.000', 2.04, 1.02, 1.53)
,('2019-06-12 00:00:00.000', 3.32, 1.66, 2.49)
,('2019-06-13 00:00:00.000', 3.16, 1.58, 2.37)
,('2019-06-14 00:00:00.000', 0.12, 0.06, 0.09)


Query:

SELECT 
    MAX(WeekEnd) AS WeekEnding,
    MAX(High) AS High,
    MIN(Low) AS Low,
    MAX([Close]) AS [Close]
FROM
(
SELECT DATEPART(WEEK, DateLogged) YearWeek, 
    LAST_VALUE(DateLogged) OVER (PARTITION BY DATEPART(WEEK, DateLogged) ORDER BY DATEPART(WEEK, DateLogged)) AS WeekEnd, 
    High,
    Low,
    LAST_VALUE([Close]) OVER (PARTITION BY DATEPART(WEEK, DateLogged) ORDER BY DATEPART(WEEK, DateLogged)) AS [Close]
FROM #DailyTable dt
) src
GROUP BY YearWeek


Results:

WeekEnding                  High    Low     Close
-------------------------------------------------
2019-06-01 00:00:00.000     2.44    1.06    1.83
2019-06-08 00:00:00.000     3.52    0.08    2.64
2019-06-14 00:00:00.000     3.40    0.06    0.09