You probably want to do something like this then:

WITH SampleData AS

(

SELECT userid, [date], usage

FROM

(

VALUES ('cjohn','2013/10/01 00:30:00',5)

,('fpears','2013/10/03 00:11:00',2)

,('cjohn','2013/10/04 12:30:45',3)

,('kthomas','2013/10/04 13:20:11',3)

,('cjohn','2013/10/04 14:10:10',2)

,('rpeter','2013/10/04 18:01:01',3)

,('cjohn','2013/10/04 19:10:01',10)

,('fpears','2013/10/06 19:11:11',11)

,('cjohn','2013/10/07 10:11:03',20)

,('rpeter','2013/10/09 05:10:05',11)

,('fpears','2013/10/11 06:10:15',6)

,('cjohn','2013/10/14 13:11:11',7)

,('kthomas','2013/10/16 08:10:10',6)

) a (userid, [date], usage)

)

SELECT userid, [date]=CAST([date] AS DATE), usage

INTO #Temp

FROM SampleData

-- By day

SELECT [date], AvgUsage=(1.0 * SUM(usage)) / COUNT(DISTINCT userid)

FROM #Temp

GROUP BY [date];

-- By week

SELECT [week]=DATEADD(week, DATEDIFF(week, 0, [date]), 0)

,AvgUsage=(1.0 * SUM(usage)) / COUNT(DISTINCT userid)

FROM #Temp

GROUP BY DATEADD(week, DATEDIFF(week, 0, [date]), 0);

-- By month

SELECT [month]=DATEADD(month, DATEDIFF(month, 0, [date]), 0)

,AvgUsage=(1.0 * SUM(usage)) / COUNT(DISTINCT userid)

FROM #Temp

GROUP BY DATEADD(month, DATEDIFF(month, 0, [date]), 0);

-- By year

SELECT [month]=DATEADD(year, DATEDIFF(year, 0, [date]), 0)

,AvgUsage=(1.0 * SUM(usage)) / COUNT(DISTINCT userid)

FROM #Temp

GROUP BY DATEADD(year, DATEDIFF(year, 0, [date]), 0);

SELECT DATEADD(week, DATEDIFF(week, 0, '2013-09-28'), 0) -- This is Sat

,DATEADD(week, DATEDIFF(week, 0, '2013-09-29'), 0) -- This is Sun

,DATEADD(week, DATEDIFF(week, 0, '2013-09-30'), 0) -- This is Mon

GO

DROP TABLE #Temp;

The only thing tricky about this is the week reporting. The final select shows that Sundays are reported in the same week as the following Monday, but the date returned by the DATEADD construct is the Monday. This is going to be sensitive to your setting for DATEFIRST.

Play around with it and see if it helps.