Eliminating Weekend Dates in an expression

Personally, I'd use a calendar table (Bones of SQL - The Calendar Table) and calculate from that..

Then, using a Function, you could do something like this (Note, my Date table is not the same as that of in the above link, but the principle is the same):
USE DevTestDB;
GO

CREATE FUNCTION WorkingDays (@StartDate DATE, @EndDate DATE)
RETURNS TABLE
AS
RETURN (
  SELECT COUNT(DT.DateKey) AS WorkingDays,
        @StartDate AS StartDate,
        @EndDate AS EndDate
  FROM DateTable DT
  WHERE DT.[Date] BETWEEN @StartDate AND @EndDate
    AND DT.[Working Day] = 1 --I have a Working day bit on my Table, which also excludes public holidays
    --AND DT.[Day Name] NOT IN ('Saturday','Sunday') --Or you can do the simple way and exclude weekends
);
GO

SELECT *
FROM WorkingDays ('01-Jan-2017',GETDATE());
/*
Result:
WorkingDays StartDate EndDate
----------- ---------- ----------
44          2017-01-01 2017-03-02
*/
GO

DROP Function WorkingDays;
GO


Thom is right - a calendar table is the way to go.  You can use it again and again, and you can customise it with stuff like public holidays.  However, if your requirement is isolated and really as simple as you say, read on.

First, let's format your code and get rid of the redundant CONVERTs.  (If you post a chunk of code that you've made no attempt to format then it'll be difficult to read, and many will take the view that it's not worth bothering with if you don't care about it.)
SELECT
     o.Customerid
,    o.Stockarrived
,    o.Status
FROM orders AS o
WHERE o.Customerid = '12345'
AND DATEDIFF(dd,o.Stockarrived,GETDATE()) - (2 * DATEDIFF(wk,o.Stockarrived,GETDATE()) = 7
ORDER BY o.Stockarrived DESC;

The next thing is to make the second part of your WHERE clause SARGable by avoiding functions on Stockarrived.  This will mean that the query optimizer will be able to consider seeking on any index on the column, and that the calculation only as to be done once - on the GETDATE() constant instead of (potentially) for every row in the table.  If it weren't for your weekend requirement, this would be quite simple:
AND o.Stockarrived >= DATEADD(day,-7,GETDATE) AND o.Stockarrived < DATEADD(day,-6,GETDATE()) -- times between midnight a week ago and (but not including) midnight six days ago

However, we do have the weeekend requirement, so we have to think of another way.  Note that your solution relies on the value of @@DATEFIRST.  Try SET LANGAUAGE 'English' and SET LANGUAGE 'British English' before running it, and see whether you get the same results each time.  What would be easier is to take off seven days, and then take off more days depending on what the day today is.  To make it look even cleaner, we could do that calculation before running the query.
DECLARE @7DaysAgo datetime;
SET @7DaysAgo = GETDATE() -7
    -    CASE DATENAME(dw,CURRENT_TIMESTAMP)
            WHEN 'Monday'    THEN 4
            WHEN 'Tuesday'   THEN 4
            WHEN 'Wednesday' THEN 2
            WHEN 'Thursday'  THEN 2
            WHEN 'Friday'    THEN 2
            WHEN 'Saturday'  THEN 3
            WHEN 'Sunday'    THEN 4
        END;
SELECT
     o.Customerid
,    o.Stockarrived
,    o.Status
FROM orders AS o
WHERE o.Customerid = '12345'
AND o.Stockarrived >= @7DaysAgo
AND o.StockArrived < @7DaysAgo + 1
ORDER BY o.Stockarrived DESC;

In the absence of any sample data, I haven't tested this, so please make sure that you're happy my day calculations are correct.  And note that, while this solution doesn't rely on @@DATEFIRST, it does rely on your langauage being English or British English!

John