Choosing values from multiple columns based on latest value of one column
EVERY Column in a SELECT has to be in the GROUP BY or use a aggregator function
SELECT  
    c.userName,
    MAX(c.DateTime),
    c.bloodPressure, 
    c.temperature
FROM CheckupData c
GROUP BY 
    c.userName,c.bloodPressure, c.temperature

OR
SELECT  
    c.userName,
    MAX(c.DateTime),
    AVG(c.bloodPressure), 
    AVG(c.temperature)
FROM CheckupData c
GROUP BY 
    c.userName

As we don't know nothing about your data and desired result. You have to choose what values you need.
For big tables you can use


CREATE TABLE CheckupData 
    ([userName] varchar(5), [DateTime] varchar(21), [bloodPressure] int, [temperature] int, [heartBeat] int, [hatSize] int)
;
    
INSERT INTO CheckupData 
    ([userName], [DateTime], [bloodPressure], [temperature], [heartBeat], [hatSize])
VALUES
    ('Curly', '&quot;2021-01-19 18:24:53&quot;', 121, 98, 60, 7.25),
    ('Larry', '&quot;2021-01-14 18:24:53&quot;', 125, 99, 80, 7.5),
    ('Mo', '&quot;2021-01-13 18:24:53&quot;', 123, 100, 70, 7.75),
    ('Curly', '&quot;2021-01-18 18:24:53&quot;', 120, 97, 50, 8),
    ('Larry', '&quot;2021-01-13 18:24:53&quot;', 119, 99, 75, 7.15),
    ('Larry', '&quot;2021-01-15 18:24:53&quot;', 115, 98, 85, 7.37),
    ('Mo', '&quot;2021-01-12 18:24:53&quot;', 110, 102, 100, 8.01),
    ('Mo', '&quot;2021-01-20 18:24:53&quot;', 130, 99, 110, 6.97),
    ('Larry', '&quot;2021-01-18 18:24:53&quot;', 127, 98, 72, 7.76),
    ('Curly', '&quot;2021-01-17 18:24:53&quot;', 126, 97, 82, 8.0)
;



GO




SELECT
cd.[userName], cd.[DateTime], cd.[bloodPressure], cd.[temperature], cd.[heartBeat], cd.[hatSize]
FROM CheckupData cd INNER JOIN 
(SELECT MAX([DateTime]) lastdate,[userName] FROM CheckupData GROUP BY [userName]) cd1
ON cd.[userName]  = cd1.[userName] AND cd.[DateTime] = cd1.lastdate
GO


userName | DateTime              | bloodPressure | temperature | heartBeat | hatSize
:------- | :-------------------- | ------------: | ----------: | --------: | ------:
Mo       | &quot;2021-01-20 18:24:53&quot; |           130 |          99 |       110 |       6
Larry    | &quot;2021-01-18 18:24:53&quot; |           127 |          98 |        72 |       7
Curly    | &quot;2021-01-19 18:24:53&quot; |           121 |          98 |        60 |       7


db&lt;&gt;fiddle here