Nested query not recognize external table
The reason for the error is explained in MySQL documentation in part E.4. Restrictions on Subqueries as:

Subqueries in the FROM clause cannot be correlated subqueries. They are materialized in whole (evaluated to produce a result set) during query execution, so they cannot be evaluated per row of the outer query.

Changing query a bit like the following seems to solve your problem:
SELECT t.CodC, c.NameC, t.Amount, t.Year, t.Week, 
    IF(t.Week!=@week OR t.Year!=@year, @rank:=1, @rank:=@rank+1) AS rank, 
    @week:=t.Week, @year:=t.Year 
FROM
    (SELECT CodC, Sum(Imports) As Amount, Year, Week
        FROM Weekly
        WHERE Year=2014
        GROUP BY CodC, Year, Week
        ORDER BY Year DESC, Week DESC, Amount DESC) t
    JOIN (SELECT @rank:=0, @week:=-1, @year:=-1) t2 ON 1
    LEFT JOIN Companies c ON c.CodC=t.CodC

It basically adds an artificial rank column by checking year and week values on the ordered rows.
Edit
Previous query is given to order by weekly sum because of misunderstanding. Following query will give what you want
SELECT t2.*,
    IF(t2.Week!=@week OR t2.Year!=@year, @rank:=1, @rank:=@rank+1) AS rank, 
    @week:=t2.Week, @year:=t2.Year 
FROM
    (SELECT t1.*, SUM(w2.Imports) AS cnt
    FROM
        (SELECT w1.CodC, c.NameC, w1.Week, w1.Year
        FROM Weekly w1
            LEFT JOIN Companies c on c.CodC=w1.CodC
            ORDER BY w1.Year ASC, w1.Week ASC) t1
            LEFT JOIN Weekly w2 ON t1.CodC=w2.CodC AND w2.Year=t1.Year AND w2.Week&lt;=t1.Week
            GROUP BY t1.CodC, t1.Week, t1.Year
            ORDER BY t1.Year DESC, t1.Week DESC, cnt DESC
            )t2
    JOIN (SELECT @rank:=0, @week:=-1, @year:=-1) t3 ON 1

Fiddle